137 results on '"delay differential equations"'
Search Results
2. Stability and Bifurcation Analysis in Turning of Flexible Parts with Spindle Speed Variation Using FEM Simulation Data.
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Shamei, Mahdi and Tajalli, Seyed Ahmad
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DELAY differential equations , *EULER-Bernoulli beam theory , *DIFFERENTIAL forms , *HOPF bifurcations , *SPEED , *EIGENVALUES - Abstract
This study investigates the effect of variable spindle speed with sinusoidal modulation on chatter vibrations generated in turning of flexible parts. The Euler–Bernoulli beam theory is assumed for mathematical modeling of the slender workpiece that is clamped at the chuck and pinned at the tailstock. The induced force as interaction between tool and workpiece (A2024-T351) during chip formation is calculated using finite element simulation. Numerical-based semi-discretization approach is utilized to seek stability regions and chatter frequencies regarding coupled dynamic model of tool and workpiece, in the form of delay differential equations with time varying delay term. The simulated data are validated and compared with those for a rigid part. The results indicate the efficiency of periodic modulation in improvement of machining stability especially for low spindle speeds. The stability charts for different interaction location and also time history response are studied, extensively. Finally, detection of period-one, flip and secondary Hopf bifurcations for different spindle speeds at instability borders are analyzed and discussed by solving corresponding eigenvalue problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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3. Hopf bifurcation and normal form in a delayed oncolytic model.
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Najm, Fatiha, Ahmed, Moussaid, Yafia, Radouane, Aziz Alaoui, M. A., and Boukrim, Lahcen
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In this paper, we investigate the mathematical analysis of a mathematical model describing the virotherapy treatment of a cancer with logistic growth and the effect of viral cycle presented by a time delay. The cancer population size is divided into uninfected and infected compartments. Depending on time delay, we prove the positivity and boundedness and the stability of equilibria. We give conditions on which the viral cycle leads to “Jeff’s phenomenon” observed in laboratory and causes oscillations in cancer size via Hopf bifurcation theory. We establish an algorithm that determines the bifurcation elements via center manifold and normal form theories. We give conditions which lead to a supercritical or subcritical bifurcation. We end with numerical simulations illustrating our theoretical results. [ABSTRACT FROM AUTHOR]
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- 2024
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4. FINITE-TIME STABILITY OF WOLBACHIA-DRIVEN MOSQUITOES BASED ON STOCHASTIC DIFFERENTIAL EQUATIONS WITH TIME-VARYING DELAY.
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GUO, WENJUAN and YU, JIANSHE
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STOCHASTIC differential equations , *DELAY differential equations , *MOSQUITOES , *BOUND states , *INFECTIOUS disease transmission , *RAINFALL - Abstract
It is well known that various environmental factors, such as temperature, rainfall and humidity, strongly influence the development and reproduction of mosquito populations and thus the transmission dynamics of mosquito-borne diseases. In this paper, a stochastic noise is introduced to describe the effects of environmental changes on mosquito population dynamics. Considering the waiting period of wild mosquitoes from mating to emergence, the finite-time stability of wild mosquitoes by releasing Wolbachia-infected mosquitoes was studied using a stochastic differential equation with time-varying delay. Finite-time stability describes the phenomenon that the bound of the state does not exceed a specified threshold at a fixed time interval. Sufficient conditions for the finite-time stability are obtained by employing the Lyapunov function and stochastic comparison theorem. Numerical simulations are also provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]
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- 2023
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5. Hopf Bifurcation, Approximate Periodic Solutions and Multistability of Some Nonautonomous Delayed Differential Equations.
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Zhang, Wenxin, Pei, Lijun, and Chen, Yueli
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HOPF bifurcations , *DELAY differential equations , *BIFURCATION diagrams , *MULTIPLE scale method , *DUFFING equations , *STATE feedback (Feedback control systems) , *DUFFING oscillators - Abstract
Research on nonautonomous delayed differential equations (DDEs) is crucial and very difficult due to nonautonomy and time delay in many fields. The main work of the present paper is to discuss complex dynamics of nonautonomous DDEs, such as Hopf bifurcation, periodic solutions and multistability. We consider three examples of nonautonomous DDEs with time-varying coefficients: a harmonically forced Duffing oscillator with time delayed state feedback and periodic disturbance, generalized van der Pol oscillator with delayed displacement difference feedback and periodic disturbance, and an electro-mechanical system with delayed and periodic disturbance. Firstly, we obtain the amplitude equations of these three examples by the method of multiple scales (MMS), and then analyze the stability of approximate solutions by the Routh–Hurwitz criterion. The obtained amplitude equations are used to construct the bifurcation diagrams, so that we can observe the occurrence of the Hopf bifurcation and judge its type (super- or subcritical) from the bifurcation diagrams. We discover rich dynamic phenomena of the three systems under consideration, such as Hopf bifurcation, quasi-periodic solutions and the coexistence of multiple stable solutions, and then discuss the impact of some parameter changes on the system dynamics. Finally, we validate the correctness of these theoretical conclusions by software WinPP, and the numerical simulations are consistent with our theoretical findings. Therefore, the MMS we use to analyze the dynamics of nonautonomous DDEs is effective, which is of great significance to the research of nonautonomous DDEs in many fields. [ABSTRACT FROM AUTHOR]
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- 2023
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6. The asymptotic behavior of solutions for stochastic evolution equations with pantograph delay.
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Liu, Yarong, Wang, Yejuan, and Caraballo, Tomas
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DELAY differential equations , *EVOLUTION equations , *FACTORIZATION , *PANTOGRAPH , *STOCHASTIC partial differential equations , *NONLINEAR evolution equations , *STOCHASTIC differential equations - Abstract
The polynomial stability problem of stochastic delay differential equations has been studied in recent years. In contrast, there are relatively few works on stochastic partial differential equations with pantograph delay. The present paper is devoted to investigating large-time asymptotic properties of solutions for stochastic pantograph delay evolution equations with nonlinear multiplicative noise. We first show that the mild solutions of stochastic pantograph delay evolution equations with nonlinear multiplicative noise tend to zero with general decay rate (including both polynomial and logarithmic rates) in the p th moment and almost sure senses. The analysis is based on the Banach fixed point theorem and various estimates involving the gamma function. Moreover, by using a generalized version of the factorization formula and exploiting an approximation technique and a convergence analysis, we construct the nontrivial equilibrium solution, defined for t ∈ ℝ , for stochastic pantograph delay evolution equations with nonlinear multiplicative noise. In particular, the uniqueness, Hölder regularity in time and general stability, in the p th moment and almost sure senses, of the nontrivial equilibrium solution are established. [ABSTRACT FROM AUTHOR]
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- 2023
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7. Multiple Periodic Solutions of Nonautonomous Delay Differential Equations.
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Li, Lin and Ge, Weigao
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DELAY differential equations , *ORBITS (Astronomy) - Abstract
In this paper, we consider a nonautonomous high-order delay differential equation with 2 r − 1 lags. The 4 r -periodic orbits are obtained by using the variational method and a new Z n index theory. This is a new type of nonautonomous delay differential equation compared with all existing ones. An example is given to demonstrate our main results. [ABSTRACT FROM AUTHOR]
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- 2023
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8. Intelligent computing networks for nonlinear influenza-A epidemic model.
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Anwar, Nabeela, Shoaib, Muhammad, Ahmad, Iftikhar, Naz, Shafaq, Kiani, Adiqa Kausar, and Raja, Muhammad Asif Zahoor
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INTELLIGENT networks , *ARTIFICIAL intelligence , *EPIDEMICS , *BIOLOGICAL mathematical modeling , *DELAY differential equations , *POPULATION dynamics - Abstract
The differential equations having delays take paramount interest in the research community due to their fundamental role to interpret and analyze the mathematical models arising in biological studies. This study deals with the exploitation of knack of artificial intelligence-based computing paradigm for numerical treatment of the functional delay differential systems that portray the dynamics of the nonlinear influenza-A epidemic model (IA-EM) by implementation of neural network backpropagation with Levenberg–Marquardt scheme (NNBLMS). The nonlinear IA-EM represented four classes of the population dynamics including susceptible, exposed, infectious and recovered individuals. The referenced datasets for NNBLMS are assembled by employing the Adams method for sufficient large number of scenarios of nonlinear IA-EM through the variation in the infection, turnover, disease associated death and recovery rates. The arbitrary selection of training, testing as well as validation samples of dataset are utilizing by designed NNBLMS to calculate the approximate numerical solutions of the nonlinear IA-EM develop a good agreement with the reference results. The proficiency, reliability and accuracy of the designed NNBLMS are further substantiated via exhaustive simulations-based outcomes in terms of mean square error, regression index and error histogram studies. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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9. Asymptotic stability in a mosquito population suppression model with time delay.
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Hui, Yuanxian, Zhao, Zhong, Li, Qiuying, and Pang, Liuyong
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LARVAL dispersal , *MOSQUITOES , *GLOBAL asymptotic stability , *DELAY differential equations - Abstract
In this paper, a delayed mosquito population suppression model, where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function, and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae, is developed and studied. A threshold value r ∗ for the releases of sterile mosquitoes is determined, and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value r ∗ . Besides, the case when the number of sterile mosquitoes released stays at a constant level r is also considered. In the special case, it is also proved that the origin is globally asymptotically stable if and only if r > r ∗ and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when r ≤ r ∗ . Numerical examples are also provided to illustrate our main theoretical results. [ABSTRACT FROM AUTHOR]
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- 2023
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10. SEMI-ANALYTICAL VIEW OF TIME-FRACTIONAL PDES WITH PROPORTIONAL DELAYS PERTAINING TO INDEX AND MITTAG-LEFFLER MEMORY INTERACTING WITH HYBRID TRANSFORMS.
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SHI, LEI, RASHID, SAIMA, SULTANA, SOBIA, KHALID, AASMA, AGARWAL, PRAVEEN, and OSMAN, MOHAMED S.
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CAPUTO fractional derivatives , *DELAY differential equations , *PARTIAL differential equations - Abstract
This paper focuses on the theoretical and computational investigation of the innovative nonlinear time-fractional PDEs incorporating the Caputo and Atangana–Baleanu fractional derivatives in the Caputo context using the q ̂ -homotopy analysis transform method (HATM). The expected strategy employs a combination of q ̂ -HATM and the Jafari transform with the assistance of Caputo and Atangana–Baleanu fractional derivative operators to obtain the methodology permits of PDEs with proportional delay. The fractional operators are employed in this research to demonstrate how crucial they are in generalizing frames involving singular and nonsingular kernels. The proposed series of solutions are closely in agreement with an exact solution. Several important challenges can be addressed to illustrate the validity of the proposed method. The outcomes of the proposed framework are displayed and assessed using numerical and graphical outputs. Furthermore, the results of our suggested strategy were compared to earlier outcomes. The proposed method requires less computation and has significantly better performance. Finally, the analysis shows that the enhanced technique is both reliable and meticulous when evaluating the impact of nonlinearities in science and technology. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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11. Global Hopf Bifurcation of State-Dependent Delay Differential Equations.
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Guo, Shangjiang
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HOPF bifurcations , *FUNCTIONAL differential equations , *DELAY differential equations - Abstract
We apply the 1 -equivariant degree method to a Hopf bifurcation problem for functional differential equations with a state-dependent delay. The formal linearization of the system at a stationary state is extracted and translated into a bifurcation invariant by using the homotopy invariance of 1 -equivariant degree. As a result, the local Hopf bifurcation is detected and the global continuation of periodic solutions is described. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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12. Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and strong kernel.
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Zhang, Xiaofeng and Yuan, Rong
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STOCHASTIC analysis , *MATHEMATICAL logic , *FOKKER-Planck equation , *BIFURCATION theory , *STOCHASTIC systems , *STOCHASTIC models , *STOCHASTIC integrals , *DELAY differential equations , *HOPF bifurcations - Abstract
Since the stochastic bifurcation theory is still in its infancy, we try to analyze some stochastic bifurcation phenomenon from a simple mathematical model. Thus, this paper mainly focuses on studying the stochastic bifurcation of a stochastic logistic model with distributed delay in the strong kernel case, which is affected by noise. Therefore, we use the intrinsic growth rate as a bifurcation parameter. First, we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model. Furthermore, by deriving the corresponding Fokker–Planck equation, we obtain the expression of the joint density function of the stochastic logistic system near the positive equilibrium point. Finally, some conclusions are given. [ABSTRACT FROM AUTHOR]
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- 2023
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13. Explicit values of the oscillation bounds for linear delay differential equations with monotone argument.
- Author
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Pituk, Mihály, Stavroulakis, Ioannis P., and Stavroulakis, John Ioannis
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LINEAR differential equations , *OSCILLATIONS , *DELAY differential equations - Abstract
The problem of finding the oscillation bounds for first-order linear delay differential equations has been in the focus of the oscillation theory for a long time. Although numerous estimates for the oscillation bounds are available in the literature, their explicit values were not known. In this paper, we give the oscillation bounds explicitly in terms of the real branches of the Lambert W function. [ABSTRACT FROM AUTHOR]
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- 2023
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14. Numerical study of chronic hepatitis B infection using Marchuk–Petrov model.
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Khristichenko, Michael, Nechepurenko, Yuri, Grebennikov, Dmitry, and Bocharov, Gennady
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CHRONIC hepatitis B , *CHRONIC active hepatitis , *HEPATITIS B , *ANTIGEN presentation , *INFECTION , *COGNITIVE computing - Abstract
In this work, we briefly describe our technology developed for computing periodic solutions of time-delay systems and discuss the results of computing periodic solutions for the Marchuk–Petrov model with parameter values, corresponding to hepatitis B infection. We identified the regions in the model parameter space in which an oscillatory dynamics in the form of periodic solutions exists. The respective solutions can be interpreted as active forms of chronic hepatitis B. The period and amplitude of oscillatory solutions were traced along the parameter determining the efficacy of antigen presentation by macrophages for T- and B-lymphocytes in the model.. The oscillatory regimes are characterized by enhanced destruction of hepatocytes as a consequence of immunopathology and temporal reduction of viral load to values which can be a prerequisite of spontaneous recovery observed in chronic HBV infection. Our study presents a first step in a systematic analysis of the chronic HBV infection using Marchuk–Petrov model of antiviral immune response. [ABSTRACT FROM AUTHOR]
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- 2023
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15. Effects of Incorporating Double Time Delays in an Investment Savings-Liquidity Preference Money Supply (IS-LM) Model.
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Rajpal, Akanksha, Bhatia, Sumit Kaur, and Kumar, Vijay
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MONEY supply , *DELAY differential equations , *BUSINESS cycles , *CAPITAL stock , *DECISION making in investments , *HOPF bifurcations - Abstract
The Investment Savings-Liquidity preference Money supply (IS-LM) model is represented as a graph depicting the intersection of products and the money market. It elaborates how an equilibrium of money supply versus interest rates may keep the economy in control. In this paper, we combine the basic business cycle IS-LM model with Kaldor's growth model in order to create an augmented model. The IS-LM model, when coupled with a certain economics expansion (in our instance, the Kaldor–Kalecki Business Cycle Model), provides a comprehensive description of a developing but robust economy. Right after the introduction of capital stock into the system, it cannot be employed and also, while making some investment choices, this requires some time in execution, which ultimately alters resources, i.e. capital. Thus, in the capital accumulation, we will be incorporating double time delays in Gross product and Capital Stock. These time delays represent the time periods during which investment decisions were made and executed and the time spent in order for the capital to be put to productive use. After formulating a mathematical model using delayed differential equations, dynamic functioning of the system around equilibrium point is examined where three instances appeared based on time delays. These cases are: when both delays are not in action, when only one delay is in action and when both delays are in action. It is shown that time delay affects the stability of the equilibrium point and, as the delay crosses a critical point, Hopf bifurcation exists. It is observed that by using Kaldor type investment function, the delay residing in capital stock only will destabilize in less time as compared to when both the delays are present in the system. The system is sensitive to certain parameters which is also analyzed in this work. [ABSTRACT FROM AUTHOR]
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- 2023
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16. Forward–backward stochastic differential equations with delay generators.
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Aman, Auguste, Coulibaly, Harouna, and Đorđević, Jasmina
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DELAY differential equations , *STOCHASTIC differential equations - Abstract
In this paper, we prove a result of existence and uniqueness of solutions to coupled forward–backward stochastic differential equations with delayed generators under a Lipschitz condition. [ABSTRACT FROM AUTHOR]
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- 2023
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17. ON EXISTENCE AND STABILITY RESULTS FOR PANTOGRAPH FRACTIONAL BOUNDARY VALUE PROBLEMS.
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ALRABAIAH, HUSSAM, ALI, GAUHAR, ALI, AMJAD, SHAH, KAMAL, and ABDELJAWAD, THABET
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BOUNDARY value problems , *NONLINEAR boundary value problems , *FRACTIONAL calculus , *EXPONENTIAL decay law , *PANTOGRAPH , *DELAY differential equations , *FRACTIONAL differential equations - Published
- 2022
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18. STUDY ON THE DYNAMICS OF A PIECEWISE TUMOR–IMMUNE INTERACTION MODEL.
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SAIFULLAH, SAYED, AHMAD, SHABIR, and JARAD, FAHD
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FIXED point theory , *DIFFERENTIAL calculus , *DELAY differential equations , *NEOVASCULARIZATION inhibitors - Published
- 2022
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19. USING THE MEASURE OF NONCOMPACTNESS TO STUDY A NONLINEAR IMPULSIVE CAUCHY PROBLEM WITH TWO DIFFERENT KINDS OF DELAY.
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SHAH, KAMAL, MLAIKI, NABIL, ABDELJAWAD, THABET, and ALI, ARSHAD
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OSCILLATION theory of differential equations , *BOUNDARY value problems , *NONLINEAR boundary value problems , *FRACTIONAL calculus , *DELAY differential equations , *IMPULSIVE differential equations , *CAUCHY problem - Published
- 2022
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20. QUALITATIVE ANALYSIS OF IMPLICIT DELAY MITTAG-LEFFLER-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS.
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YAO, SHAO-WEN, SUGHRA, YASMEEN, ASMA, INC, MUSTAFA, and ANSARI, KHURSHEED J.
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FRACTIONAL differential equations , *LIFE sciences , *DELAY differential equations , *DERIVATIVES (Mathematics) , *DIFFERENTIAL calculus , *ADVECTION-diffusion equations , *DIFFERENTIAL operators - Published
- 2022
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21. Lie symmetry analysis of time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays.
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Yu, Jicheng
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REACTION-diffusion equations , *KORTEWEG-de Vries equation , *BURGERS' equation , *FRACTIONAL differential equations , *ORDINARY differential equations , *PARTIAL differential equations , *DELAY differential equations - Abstract
In this paper, Lie symmetry analysis method is applied to time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays, respectively. The Lie symmetries for fractional partial differential equations with delays (DFPDEs) are obtained, and the group classifications of the equations are established. The obtained group generators are used to reduce the DFPDEs to fractional ordinary differential equations with delays (DFODEs). Some exact solutions constructed for the DFODEs generate group-invariant solutions of the discussed DFPDEs. [ABSTRACT FROM AUTHOR]
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- 2022
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22. Author index Volume 22.
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EULER method , *DELAY differential equations , *DIFFERENCE equations , *LOTKA-Volterra equations , *STOCHASTIC partial differential equations , *STOCHASTIC differential equations , *FRACTIONAL differential equations , *INTEGRO-differential equations , *MATHEMATICAL analysis - Published
- 2022
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23. Complex dynamics of Leslie–Gower prey–predator model with fear, refuge and additional food under multiple delays.
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Gupta, Ashvini, Kumar, Ankit, and Dubey, Balram
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DELAY differential equations , *SYSTEM dynamics - Abstract
In this paper, we analyze a system of delay differential equations incorporating prey's refuge, fear, fear-response delay, extra food for predators and their gestation lag. First, we examined the system without delay. The persistence, stability (local and global) and various bifurcations are discussed. We provide detailed analysis for transcritical and Hopf-bifurcation. The existence of positive equilibria and the stability of prey-free equilibrium are interrelated. It is shown that (i) fear can stabilize or destabilize the system, (ii) prey refuge in a specific limit can be advantageous for both species, (iii) at a lower energy level (gained from extra food), the system undergoes a supercritical Hopf-bifurcation and (iv) when the predator gains high energy from extra food, it can survive through a homoclinic bifurcation, and prey may become extinct. The possible occurrence of bi-stability with or without delay is discussed. We observed switching of stability thrice via subcritical Hopf-bifurcation for fear-response delay. On changing some parametric values, the system undergoes a supercritical Hopf-bifurcation for both delay parameters. The delayed system undergoes the Hopf-bifurcation, so we can say that both delay parameters play a vital role in regulating the system's dynamics. The analytical results obtained are verified with the numerical simulation. [ABSTRACT FROM AUTHOR]
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- 2022
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24. Queues with Delayed Information: Analyzing the Impact of the Choice Model Function.
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Doldo, Philip and Pender, Jamol
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LOGISTIC regression analysis , *DELAY differential equations , *DISCRETE choice models - Abstract
In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is exponential. However, in this work we generalize this to different functional forms. In particular, we compute the critical delay and analyze how it depends on the choice of the functional form. We highlight how the functional form of the model can be interpreted as an exponential model where the exponential rate parameter is uncertain. Furthermore, the rate parameter distribution is given by the inverse Laplace–Stieltjes transform of the functional form when it exists. We perform numerous numerical experiments to confirm our theoretical insights. [ABSTRACT FROM AUTHOR]
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- 2022
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25. Endless Process of Bifurcations in Delay Differential Equations.
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NONLINEAR differential equations , *PARTIAL differential equations , *DELAY differential equations , *SINGULAR perturbations - Abstract
The paper is devoted to studying the singularly perturbed equations and systems with one or multiple delays. In focus is a bifurcation effect that, as the small parameter present in the system tends to zero, an endless process of forward and backward bifurcations repetition occur. To describe this effect and give its analytical background, we use the analog of the normal form, the quasinormal form, a nonlinear partial differential equation that regularly depends on a small parameter. The solutions of the quasinormal form give the main part of the asymptotic approximation of the solution of the differential equation with delay. Also effects of endless process of bifurcations is demonstrated in detail in two examples. In the first example, we consider second order equation with large delay, and in the second example — first order equation with two delays. [ABSTRACT FROM AUTHOR]
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- 2022
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26. k-Nearest Neighbor Queues with Delayed Information.
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K-nearest neighbor classification , *HOPF bifurcations , *CIRCULANT matrices , *STABILITY theory , *QUEUING theory , *DELAY differential equations , *LIMIT cycles - Abstract
In this paper, we analyze a model called the k-nearest neighbor queue with the possibility of having delayed queue length feedback. We prove fluid limits for the stochastic queueing model and show that the fluid limit converges to a system of delay differential equations. Using the properties of circulant matrices, we derive a closed form expression for the value of the critical delay, which governs whether the delayed information will induce oscillations or a Hopf bifurcation in our queueing system. [ABSTRACT FROM AUTHOR]
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- 2022
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27. Hopf Bifurcation in Oncolytic Therapeutic Modeling: Viruses as Anti-Tumor Means with Viral Lytic Cycle.
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Najm, Fatiha, Yafia, Radouane, and Aziz-Alaoui, M. A.
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LYTIC cycle , *HOPF bifurcations , *ONCOLYTIC virotherapy , *DELAY differential equations , *VIRAL transmission , *CELL populations - Abstract
In this paper, we propose a delayed mathematical model describing oncolytic virotherapy treatment of a tumour that proliferates according to the logistic growth function, incorporating viral lytic cycle. The tumour population cells are divided into uninfected and infected cell sub-populations and the virus spreading is supposed to be in a direct mode (i.e. from cell to cell). Depending on the time delay, we analyze the positivity and boundedness of solutions and the stability of tumour, infected and uninfected free equilibria (TFE, IFE, UFE) and uninfected–infected equilibrium (UIE) is established. We prove that, delay can lead to "Jeff's phenomenon" observed in a laboratory which causes oscillations in tumour size whose phase and period change over time. With nonlinear dependence of UIE equilibrium on time delay, we develop a more general algorithm determining the stability/instability of the oscillating periodic solutions bifurcating from the UIE equilibrium. Finally, we present numerical simulations illustrating our theoretical results. [ABSTRACT FROM AUTHOR]
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- 2022
- Full Text
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28. Stochastic P-Bifurcation in a Delayed Myc/E2F/miR-17-92 Network.
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Han, Zikun, Wang, Qiubao, Wu, Hao, and Hu, Zhouyu
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HOPF bifurcations , *STOCHASTIC systems , *NUMERICAL analysis , *STOCHASTIC analysis , *RANDOM noise theory , *DELAY differential equations , *WHITE noise - Abstract
In this paper, Myc/E2F/miR-17-92 network under Gaussian white noise is studied. Taking the time delay as the parameter, the Hopf bifurcation of the system is obtained, which causes the protein concentration to oscillate periodically. Under the influence of time delay and noise, the stochastic D-bifurcation of the system is obtained. It is worth noting that the occurrence of stochastic P-bifurcation is successfully captured. Thus a pattern of coexistence of high and low protein concentrations is founded in the network. The specific research methods of this paper are as follows: firstly, the system is reduced to a finite dimensional system by using stochastic center manifold and normal form theory. Then, using the stochastic averaging method, the Fokker–Planck–Kolmogorov equation of the system is constructed in which the statistical response in the stationary state is the probability density. Finally, the stochastic bifurcation analysis and numerical simulation are carried out. The agreements between the analytical method and those obtained numerically validate the effectiveness of the analytical investigations. [ABSTRACT FROM AUTHOR]
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- 2022
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29. Modeling the transmission dynamics of plant viral disease using two routes of infection, nonlinear terms and incubation delay.
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Al Basir, Fahad and Ray, Santanu
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VIRUS diseases , *PLANT diseases , *BASIC reproduction number , *DELAY differential equations , *DISEASE resistance of plants , *INFECTIOUS disease transmission , *REPRODUCTION - Abstract
Plant viral diseases have devastating effects on agricultural products worldwide. In this research, a delay differential equation model has been proposed for the transmission dynamics of plant viral disease using the vector-to-plant (primary) transmission and plant-to-plant (i.e. secondary) transmissions modeled via nonlinear (saturated) terms. Also, a time delay is considered in the model due to the incubation period of the plant. Feasibility and stability analyses of the equilibria of the model have been provided based on the basic reproduction numbers. Stability changes occur through Hopf bifurcation in both the delayed and non-delayed systems. Sensitivity analysis shows the impact of a parameter on the infection. The mathematical analysis of the model and numerical examples suggested that the disease will occur if the incubation period of the plant is small. Viral disease of a plant can be controlled by maintaining the distance between plants, removing the infected plants, and increasing crop resistance towards the disease. [ABSTRACT FROM AUTHOR]
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- 2022
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30. The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise.
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Liu, Yarong, Wang, Yejuan, and Caraballo, Tomás
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RANDOM noise theory , *FRACTIONAL powers , *STOCHASTIC integrals , *EQUATIONS , *DELAY differential equations , *POLYNOMIALS , *CONTINUITY , *NAVIER-Stokes equations , *BROWNIAN motion - Abstract
We consider stochastic 2D-Stokes equations with unbounded delay in fractional power spaces and moments of order p ≥ 2 driven by a tempered fractional Brownian motion (TFBM) B σ , λ (t) with − 1 / 2 < σ < 0 and λ > 0. First, the global existence and uniqueness of mild solutions are established by using a new technical lemma for stochastic integrals with respect to TFBM in the sense of p th moment. Moreover, based on the relations between the stochastic integrals with respect to TFBM and fractional Brownian motion, we show the continuity of mild solutions in the case of λ → 0 , σ ∈ (− 1 / 2 , 0) or λ > 0 , σ → σ 0 ∈ (− 1 / 2 , 0). In particular, we obtain p th moment Hölder regularity in time and p th polynomial stability of mild solutions. This paper can be regarded as a first step to study the challenging model: stochastic 2D-Navier–Stokes equations with unbounded delay driven by tempered fractional Gaussian noise. [ABSTRACT FROM AUTHOR]
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- 2022
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31. Bifurcation Analysis for Two-Species Commensalism (Amensalism) Systems with Distributed Delays.
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Li, Tianyang and Wang, Qiru
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HOPF bifurcations , *COMMENSALISM , *DELAY differential equations - Published
- 2022
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32. Immune–Pathogen Dynamics.
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RED , *DELAY differential equations , *LEUCOCYTES - Published
- 2022
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33. On the formulation of size-structured consumer resource models (with special attention for the principle of linearized stability).
- Author
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Barril, Carles, Calsina, Àngel, Diekmann, Odo, and Farkas, József Z.
- Subjects
- *
ORDINARY differential equations , *PARTIAL differential equations , *NONLINEAR operators , *BIRTH rate , *DELAY differential equations , *PROOF of concept - Abstract
To describe the dynamics of a size-structured population and its unstructured resource, we formulate bookkeeping equations in two different ways. The first, called the PDE formulation, is rather standard. It employs a first-order partial differential equation, with a non-local boundary condition, for the size-density of the consumer, coupled to an ordinary differential equation for the resource concentration. The second is called the DELAY formulation and employs a renewal equation for the population level birth rate of the consumer, coupled to a delay differential equation for the (history of the) resource concentration. With each of the two formulations we associate a constructively defined semigroup of nonlinear solution operators. The two semigroups are intertwined by a non-invertible operator. In this paper, we delineate in what sense the two semigroups are equivalent. In particular, we (i) identify conditions on both the model ingredients and the choice of state space that guarantee that the intertwining operator is surjective, (ii) focus on large time behavior and (iii) consider full orbits, i.e. orbits defined for time running from − ∞ to + ∞. Conceptually, the PDE formulation is by far the most natural one. It has, however, the technical drawback that the solution operators are not differentiable, precluding rigorous linearization. (The underlying reason for the lack of differentiability is exactly the same as in the case of state-dependent delay equations: we need to differentiate with respect to a quantity that appears as argument of a function that may not be differentiable.) For the delay formulation, one can (under certain conditions concerning the model ingredients) prove the differentiability of the solution operators and establish the Principle of Linearized Stability. Next, the equivalence of the two formulations yields a rather indirect proof of this principle for the PDE formulation. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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- View/download PDF
34. An averaging principle for neutral stochastic fractional order differential equations with variable delays driven by Lévy noise.
- Author
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Shen, Guangjun, Wu, Jiang-Lun, Xiao, Ruidong, and Yin, Xiuwei
- Subjects
- *
FRACTIONAL differential equations , *STOCHASTIC orders , *STOCHASTIC differential equations , *DELAY differential equations , *NOISE - Abstract
In this paper, we establish an averaging principle for neutral stochastic fractional differential equations with non-Lipschitz coefficients and with variable delays, driven by Lévy noise. Our result shows that the solutions of the equations concerned can be approximated by the solutions of averaged neutral stochastic fractional differential equations in the sense of convergence in mean square. As an application, we present an example with numerical simulations to explore the established averaging principle. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
35. Subcritical Neimark–Sacker bifurcation and hybrid control in a discrete-time Phytoplankton–Zooplankton model.
- Author
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Khan, A. Q. and Javaid, M. B.
- Subjects
- *
BIFURCATION diagrams , *LOTKA-Volterra equations , *PLANKTON populations , *VITAMIN B12 , *PHYTOPLANKTON populations , *DELAY differential equations , *FIXED point theory - Published
- 2022
- Full Text
- View/download PDF
36. Multidelay Differential Equations: A Taylor Expansion Approach.
- Author
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Doldo, Philip and Pender, Jamol
- Subjects
- *
TAYLOR'S series , *DIFFERENTIAL equations , *DELAY differential equations , *SYSTEM dynamics - Abstract
It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the critical delay is important to understanding the dynamics of delayed systems and is often simple to obtain when the system only has a single constant delay. However, if we consider a system with multiple constant delays, there is no known way to obtain such a formula that determines for what values of the delays a change in stability occurs. In this paper, we present some single-delay approximations to a multidelay system obtained via a Taylor expansion as well as formulas for their critical delays which are used to approximate where the change in stability occurs in the multidelay system. We determine when our approximations perform well and we give extra analytical and numerical attention to the two-delay and three-delay settings. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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- View/download PDF
37. STUDY OF FRACTIONAL ORDER DELAY CAUCHY NON-AUTONOMOUS EVOLUTION PROBLEMS VIA DEGREE THEORY.
- Author
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KHAN, ZAREEN A., SHAH, KAMAL, MAHARIQ, IBRAHIM, and ALRABAIAH, HUSSAM
- Subjects
- *
TOPOLOGICAL degree , *DELAY differential equations , *CAPUTO fractional derivatives , *CAUCHY problem , *NONLINEAR functions - Abstract
This work is devoted to derive some existence and uniqueness (EU) conditions for the solution to a class of nonlinear delay non-autonomous integro-differential Cauchy evolution problems (CEPs) under Caputo derivative of fractional order. The required results are derived via topological degree method (TDM). TDM is a powerful tool which relaxes strong compact conditions by some weaker ones. Hence, we establish the EU under the situation that the nonlinear function satisfies some appropriate local growth condition as well as of non-compactness measure condition. Furthermore, some results are established for Hyers–Ulam (HU) and generalized HU (GHU) stability. Our results generalize some previous results. At the end, by a pertinent example, the results are verified. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
38. On the geometric ergodicity for a generalized IFS with probabilities.
- Author
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Guzik, Grzegorz and Kapica, Rafał
- Subjects
- *
STOCHASTIC difference equations , *PROBABILITY measures , *STOCHASTIC processes , *MARKOV operators , *PROBABILITY theory , *BOREL sets , *DELAY differential equations - Abstract
Main goal of this paper is to formulate possibly simple and easy to verify criteria on existence of the unique attracting probability measure for stochastic process induced by generalized iterated function systems with probabilities (GIFSPs). To do this, we study the long-time behavior of trajectories of Markov-type operators acting on product of spaces of Borel measures on arbitrary Polish space. Precisely, we get the desired geometric rate of convergence of sequences of measures under the action of such operator to the unique distribution in the Hutchinson–Wasserstein distance. We apply the obtained results to study limiting behavior of random trajectories of GIFSPs as well as stochastic difference equations with multiple delays. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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39. Author index Volume 21.
- Subjects
- *
DELAY differential equations , *MULTIFRACTALS , *IMPULSIVE differential equations , *STOCHASTIC differential equations , *STOCHASTIC partial differential equations , *PARABOLIC differential equations , *DEGENERATE parabolic equations , *FRACTIONAL differential equations - Published
- 2021
- Full Text
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40. Distribution-dependent stochastic differential delay equations in finite and infinite dimensions.
- Author
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Heinemann, Rico
- Subjects
- *
STOCHASTIC differential equations , *FINITE, The , *DELAY differential equations , *PROBABILITY measures - Abstract
We prove that distribution-dependent (also called McKean–Vlasov) stochastic delay equations of the form d X (t) = b (t , X t , ℒ X t ) d t + σ (t , X t , ℒ X t ) d W (t) have unique (strong) solutions in finite as well as infinite-dimensional state spaces if the coefficients fulfill certain monotonicity assumptions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
41. DESIGN OF NEURO-SWARMING HEURISTIC SOLVER FOR MULTI-PANTOGRAPH SINGULAR DELAY DIFFERENTIAL EQUATION.
- Author
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SABIR, ZULQURNAIN, BALEANU, DUMITRU, RAJA, MUHAMMAD ASIF ZAHOOR, and GUIRAO, JUAN L. G.
- Subjects
- *
PARTICLE swarm optimization , *STANDARD deviations , *ARTIFICIAL neural networks , *ALGORITHMS , *HEURISTIC , *DELAY differential equations - Abstract
This research work is to design a neural-swarming heuristic procedure for numerical investigations of Singular Multi-Pantograph Delay Differential (SMP-DD) equation by applying the function approximation aptitude of Artificial Neural Networks (ANNs) optimized efficient swarming mechanism based on Particle Swarm Optimization (PSO) integrated with convex optimization with Active Set (AS) algorithm for rapid refinements, named as ANN-PSO-AS. A merit function (MF) on mean squared error sense is designed by using the differential ANN models and boundary condition. The optimization of this MF is executed with the global PSO and local search AS approaches. The planned ANN-PSO-AS approach is instigated for three different SMP-DD model-based equations. The assessment with available standard results relieved the effectiveness, robustness and precision that is further authenticated through statistical investigations of Variance Account For, Root Mean Squared Error, Semi-Interquartile Range and Theil's inequality coefficient performances. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
42. Global Stability and Hopf Bifurcation for a Stage Structured Model with Competition for Food.
- Author
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Lv, Yunfei, Pei, Yongzhen, and Yuan, Rong
- Subjects
- *
DELAY differential equations , *HOPF bifurcations , *PARTIAL differential equations - Abstract
Considering the mature condition of any individual to have eaten a specific amount of food during the entire period that it can spend at its immature stage, we propose a size-structured model by a first-order quasi-linear partial differential equation. The model can be firstly reduced to a single state-dependent delay differential equation and then to a constant delay differential equation. The state-dependent delay represents intra-specific competition among individuals for limited food resources. A complete analysis of the global dynamics on the positivity and boundedness of solutions, global stability for each equilibrium and Hopf bifurcation is carried out. Our results imply that the delay leads to instability that is shown by a simple example of a certain structured population model. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
43. Two-Dimensional Manifolds of Modified Chen System with Time Delay.
- Author
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Suqi, Ma
- Subjects
- *
LIMIT cycles , *DELAY differential equations , *FOLIATIONS (Mathematics) , *TIME delay systems - Abstract
Two-dimensional unstable manifolds of the modified Chen system are constructed at equilibrium solution by "expanding up" along the unstable eigen-direction, hence it is tangent to the unstable eigenspace. In general, unstable manifold expands to the attraction basin of the corresponding limit cycle or attractor. With the introduction of time delay, the two-dimensional unstable manifold of an unstable focus is simulated via expanding solution orbits with restriction condition on the associated foliations. The simulated unstable manifold coincides with the attraction basin of the limit cycle of the delay differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
44. Breaking the Symmetry in Queues with Delayed Information.
- Author
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Doldo, Philip, Pender, Jamol, and Rand, Richard
- Subjects
- *
SYMMETRY breaking , *MULTIPLE scale method , *DELAY differential equations , *DYNAMICAL systems , *HOPF bifurcations - Abstract
Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
45. Hopf Bifurcations in Nicholson's Blowfly Equation are Always Supercritical.
- Author
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Balázs, István and Röst, Gergely
- Subjects
- *
HOPF bifurcations , *BLOWFLIES , *DELAY differential equations , *EQUATIONS - Abstract
We prove that all Hopf bifurcations in the Nicholson's blowfly equation are supercritical as we increase the delay. Earlier results treated only the first bifurcation point, and to determine the criticality of the bifurcation, one needed to substitute the parameters into a lengthy formula of the first Lyapunov coefficient. With our result, there is no need for such calculations at any bifurcation point. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
46. Comparison between two tritrophic food chain models with multiple delays and anti-predation effect.
- Author
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Sahoo, Debgopal and Samanta, G. P.
- Subjects
- *
FOOD chains , *DELAY differential equations , *TOP predators , *PREDATION , *BIOMASS conversion - Abstract
Exploring the predator–prey linkage in food chain system is the most familiar research work in population biology. Recently, some research experiments show that predator–prey interaction not only governed by direct hunting but also influenced by some indirect effect such as fear effect (felt by prey) that may change the physiological behavior of prey. Based upon this fact, we consider a tritrophic food chain model incorporating with anti-predation response (fear effect) and multiple time delays for biomass conversion from prey to middle predator and middle to top predator. We analyze the resulting delay differential equations and explore how the anti-predation response level affects the population dynamics. We also investigate the effect of delay parameters, for which the model system switches its stability through Hopf-bifurcation. We compare all of our results between two different food chain models consisting of two different functional responses. Some numerical simulations are performed to validate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
47. Dynamics of Wild and Sterile Mosquito Population Models with Delayed Releasing.
- Author
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Cai, Li-Ming
- Subjects
- *
MOSQUITO control , *MOSQUITO vectors , *DELAY differential equations , *MOSQUITOES , *ORDINARY differential equations , *ARBOVIRUS diseases , *HOPF bifurcations - Abstract
To reduce the global burden of mosquito-borne diseases, e.g. dengue, malaria, the need to develop new control methods is to be highlighted. The sterile insect technique (SIT) and various genetic modification strategies, have a potential to contribute to a reversal of the current alarming disease trends. In our previous work, the ordinary differential equation (ODE) models with different releasing sterile mosquito strategies are investigated. However, in reality, implementing SIT and the releasing processes of sterile mosquitos are very complex. In particular, the delay phenomena always occur. To achieve suppression of wild mosquito populations, in this paper, we reassess the effect of the delayed releasing of sterile mosquitos on the suppression of interactive mosquito populations. We extend the previous ODE models to the delayed releasing models in two different ways of releasing sterile mosquitos, where both constant and exponentially distributed delays are considered, respectively. By applying the theory and methods of delay differential equations, the effect of time delays on the stability of equilibria in the system is rigorously analyzed. Some sustained oscillation phenomena via Hopf bifurcations in the system are observed. Numerical examples demonstrate rich dynamical features of the proposed models. Based on the obtained results, we also suggest some new releasing strategies for sterile mosquito populations. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
48. Persistence and extinction of Markov switched stochastic Nicholson's blowflies delayed differential equation.
- Author
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Wentao Wang and Wei Chen
- Subjects
- *
DELAY differential equations , *BLOWFLIES , *LOTKA-Volterra equations , *BIOLOGICAL extinction - Abstract
In this paper, we study the persistence and extinction of Markov switched stochastic Nicholson's blowflies delayed differential equation. We derive sufficient conditions of persistence and extinction for blowflies population, respectively, which solve one of open problems proposed by Zhu et al. [Stochastic Nicholson's blowflies delay differential equation with regime switching, Appl. Math. Lett. 94 (2019) 187-195]. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
49. Chaotic dynamics of a delayed tumor–immune interaction model.
- Author
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Khajanchi, Subhas
- Subjects
- *
HOPF bifurcations , *TUMOR growth , *MATHEMATICAL models , *DELAY differential equations , *BIOLOGICAL systems , *MATHEMATICIANS - Abstract
Due to the unpredictable growth of tumor cells, the tumor–immune interactive dynamics continues to draw attention from both applied mathematicians and oncologists. Mathematical modeling is a powerful tool to improve our understanding of the complicated biological system for tumor growth. With this goal, we report a mathematical model which describes how tumor cells evolve and survive the brief encounter with the immune system mediated by immune effector cells and host cells which includes discrete time delay. We analyze the basic mathematical properties of the considered model such as positivity of the system and the boundedness of the solutions. By analyzing the distribution of eigenvalues, local stability analysis of the biologically feasible equilibria and the existence of Hopf bifurcation are obtained in which discrete time delay is used as a bifurcation parameter. Based on the normal form theory and center manifold theorem, we obtain explicit expressions to determine the direction of Hopf bifurcation and the stability of Hopf bifurcating periodic solutions. Numerical simulations are carried out to illustrate the rich dynamical behavior of the delayed tumor model. Our model simulations demonstrate that the delayed tumor model exhibits regular and irregular periodic oscillations or chaotic behaviors, which indicate the scenario of long-term tumor relapse. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
50. Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay.
- Author
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Ma, Xiao, Shu, Xiao-Bao, and Mao, Jianzhong
- Subjects
- *
STOCHASTIC differential equations , *DELAY differential equations , *FUNCTIONAL differential equations , *STOCHASTIC difference equations , *FRACTIONAL calculus , *IMPULSIVE differential equations , *FRACTIONAL differential equations - Abstract
In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
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