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In this paper, a new delayed fractional-order model including susceptible migratory birds, infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds. Fear of predators is considered in the model, as fear can reduce the reproduction rate and disease transmission rate among prey. First, some basic mathematical results of the proposed model are discussed. Then, time delay is regarded as a bifurcation parameter, and the delay-induced bifurcation conditions for such an uncontrolled system are established. A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon. It is found that the control scheme can successfully suppress the bifurcation behavior of the system, and the pulse width can be arbitrarily selected on the premise of ensuring the control effect. Compared with the traditional time-delay feedback controller, the control scheme proposed in this paper has more advantages in practical application, which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment. The proposed control scheme, in particular, remains effective even after the system has been disrupted by a constant. Numerical simulation verifies the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper examines a three-dimensional delayed discrete neural network model analytically and numerically to determine the existence of different types of bifurcations of the involved fixed points. The model exhibits different bifurcations such as pitchforks, flips, Neimark–Sackers, and flip-Neimark–Sackers. The critical coefficients are used to determine the structure of each bifurcation. The curves are calculated and plotted for each bifurcation when the parameters are changed. Further, these bifurcations are theoretically analyzed and numerically verified. From the obtained results, we observed that by drawing the curves associated with each bifurcation, the numerical simulations are consistent with the analytical results. [ABSTRACT FROM AUTHOR]

This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper, we solved a model of a well-known infectious disease called dengue fever via fractional natural decomposition and modified Predictor–Corrector (PC) methods. A study of the dengue epidemic in the Cape Verde Islands off the coast of West Africa in 2009 has been resumed here for a better understanding of the results. The results are obtained using Liouville–Caputo and new generalized Caputo-type fractional derivatives. The numerical simulations are presented for various orders of given derivatives. Existence and uniqueness analysis of the given problem are also performed in the new generalized Caputo sense. The explored results are verified using figures. The main target of this paper is to explore the different dynamics of the given dengue fever model via two types of fractional numerical algorithms. [ABSTRACT FROM AUTHOR]

Active suspension technique normally provides the best vibration mitigation performance at the cost of high-energy consumption. In contrast, the energy consumption of a semi-active suspension is normally much smaller than that of an active suspension, whereas the control performance is compromised as well. Observing the core issue that caused such a phenomenon is that the existing semi-active control force, unlike the active control force, shall always oppose to the relative motion of the actuator (i.e. clipping phenomenon). This paper subsequently proposes a novel semi-active vehicle suspension system that incorporates a passive negative stiffness (NS) spring and a semi-active damper (SD) to realize uncompromised active control force while consuming energy of a typical semi-active suspension system. In specific, the proposed system allows for decomposition of the target active control force and tracked via the collaboration of the NS and SD components. Herein, the NS element is capable of releasing the store potential energy that subsequently eases the aforementioned clipping phenomenon of a traditional semi-active suspension. In this paper, besides the relevant clarifications on the system topology and working mechanism, its feasibility and performance enhancement are also validated via systematic numerical simulations of a vehicle suspension; and the results indicate, for the first time, that the proposed semi-active suspension can fully track the active control force and subsequently achieve unprecedented control performance comparable to an active controller. [ABSTRACT FROM AUTHOR]

Thin-walled composite cylindrical shells are nowadays widely used as primary structures in the aerospace industry. The so-called variable stiffness (VS) composite cylindrical shells with flexible stiffness tailoring characteristics have been made possible by existing AFP techniques. Considering the inherent imperfection sensitivity property of axially compressed thin-walled cylindrical shells, the buckling behaviors of the axially compressed VS composite cylindrical shells with initial geometric imperfections and delamination imperfections are investigated respectively in this paper. The design buckling loads of the axially compressed VS composite cylindrical shells are first determined by the probing method, which is verified by comparing with the existing test data and numerical simulation results. Additionally, a parametric study is conducted to investigate the effects of delamination imperfections on the buckling loads. The constraint delamination sizes of the VS composite cylindrical shells based on the design buckling load in this paper are given. Furthermore, the effects of continuously variable fiber angles on the buckling loads are investigated considering the imperfection sensitivity. The specific VS composite cylindrical shells with both high- buckling loads and low-imperfection sensitivity are obtained. Results indicate that the effects of imperfection sensitivity need to be carefully considered in buckling design of the axially compressed VS composite cylindrical shells. [ABSTRACT FROM AUTHOR]

The regularized lattice Boltzmann method (RLBM) has the advantage of improving the accuracy of numerical simulations without increasing the computational overhead. The RLBM usually uses the standard Cartesian grid in numerical simulation. This paper introduces the multi-layer grid technique, the multi-layer grid has different resolutions, which is also more consistent with the physical laws of the flow field. Based on this, a multi-layer grid regularized lattice Boltzmann method (ML-RLBM) for solving complex flow problems is proposed. The proposed method performs local refinement of the grid on the standard Cartesian grid to achieve a multi-layer grid, which can reduce the computational overhead. In order to realize the local grid refinement easily, this paper adopts the center point format to store the multi-layer grid. The ML-RLBM designs a buffer scheme between different layers of grids, which realizes that only spatial interpolation is required at the interface of different layers of grids without temporal interpolation. The numerical results show that the ML-RLBM has excellent numerical accuracy and numerical stability, and it can effectively reduce the computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fractal nature of the local fractional Landau–Ginzburg–Higgs Equation (LFLGHE) describing nonlinear waves with weak scattering in a fractal medium. The main goal of the paper is to introduce and apply the Local Fractional Elzaki Variational Iteration Method (LFEVIM) for solution of LFLGHE. Convergence analysis of LFEVIM solution for general nonlinear local fractional partial differential equation is also provided. Two examples of the local fractional LFLGHE are considered to demonstrate the applicability of the proposed technique with numerical simulations on Cantor set. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Leslie–Gower type reaction–diffusion predator–prey system with an increasing functional response. We mainly study the effect of three different types of diffusion on the stability of this system. The main results are as follows: (1) in the absence of prey diffusion, diffusion-driven instability can occur; (2) in the absence of predator diffusion, diffusion-driven instability does not occur and the non-constant stationary solution exists and is unstable; (3) in the presence of both prey diffusion and predator diffusion, the system can occur diffusion-driven instability and Turing patterns. At the same time, we also get the existence conditions of the Hopf bifurcation and the Turing–Hopf bifurcation, along with the normal form for the Turing–Hopf bifurcation. In addition, we conduct numerical simulations for all three cases to support the results of our theoretical analysis. [ABSTRACT FROM AUTHOR]

Hydrogen has received widespread attention as a new clean energy in order to reduce the carbon emissions of fuel vehicles. This paper studies a tubular microreactor based on methanol steam reforming. Methanol and steam are mixed in proportion and the chemical reaction takes place in a porous catalytic bed. For heating purposes, hot gas from the burner penetrates the reactor bed through heating tubes. Energy is supplied through the heating tubes to drive the endothermic reaction system. The microreactor is enclosed in an insulated jacket. In this paper, parameters such as methanol conversion and hydrogen concentration are evaluated by considering microreactor materials, heating gas temperature and flow direction, heating tube distribution, pressure drop and reaction channel length. First of all, choosing a microreactor material with a smaller thermal conductivity can avoid excessive heat loss, and improve heat transfer performance. Increasing the heating gas temperature leads to an increase in the temperature of the reaction zone, thereby increasing the CH3OH conversion rate and H2 mass fraction. Changing the flow direction of the heating gas affects the reaction rate, but has little effect on the reaction result. Through the research on the distribution of the heating tubes, the results show that the hydrogen production rate is higher when the contact area between the heating tubes and the reaction zone is larger. Secondly, through the comparison of the data under different pressure drops, the best parameter P = 5 0 pa is obtained, and the CH3OH conversion rate is 80.6% at this time. Finally, increasing the length of the reaction channel can make the reaction more complete. For example, when the reaction channel length L = 0. 3 9 m, the CH3OH conversion rate is as high as 83.7%. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for a solid spherically symmetric vascular tumor growth with nutrient periodic supply and time delays is studied. Compared to the apoptosis process of tumor cells, there is a time delay in the process of tumor cell division. The cells inside the tumor obtain nutrient σ(r,t) through blood vessels, and the tumor attracts blood vessels at a rate proportional to α(t). So, the boundary value condition ∂σ ∂r + α(t)(σ − ψ(t)) = 0,r = R(t),t > 0, holds on the boundary, where the function ψ(t) is the concentration of nutrient externally supplied to the tumor. Considering that the nutrients provided by the outside world are often periodic, the research in this paper assumes that ψ(t) is a periodic function. Sufficient conditions for the global stability of zero steady state are presented. Under certain conditions, we prove that there exists at least one periodic solution to the model. The results are illustrated by computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a discrete-time fractional-order population model are considered. The stability analysis and the topological classification of the model at the fixed point have been investigated. It is shown that the model undergoes flip and Neimark–Sacker bifurcations around the co-existence fixed point by using the bifurcation and the normal form theory. These bifurcations lead to chaos when the parameter changes at critical point. In order to control chaotic behavior in the model result from Neimark–Sacker bifurcation, the OGY feedback method has been used. Furthermore, some numerical simulations, including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the presented model are plotted to support the correctness of the analytical results. The positive Lyapunov exponents demonstrate that chaotic behavior exists in the considered model. [ABSTRACT FROM AUTHOR]

In this paper, we aim to minimize the epidemic size of tungiasis disease and economic costs simultaneously, with terminal demands for infected humans. A human–jigger parasite control system with four control schemes for humans and jiggers is established. We propose a multi-objective optimal control problem with terminal constraints, in which the accumulated number of infected humans and control costs are involved. By applying the modified normal boundary intersection algorithm and the interior point scheme, numerical simulations for different combinations of control schemes are carried out, and actual data in Madagascar are used. Effective combination schemes are indicated from the perspectives of disease eradication, cost saving and time saving. Once these effective combinations are properly performed, the disease can be controlled. When only minimizing the epidemic size, the combination of the optimal treatments and adulticiding efforts is the best choice in the rainy season; the combination of the optimal personal protections and treatments is the preferential option in the dry season. When only minimizing the economical cost, the combination of the optimal adulticide and larvicide is the better selection in the rainy season; the combination of the optimal personal protections, treatments and adulticiding efforts is the prior choose in the dry season. Thus, there is a trade-off between the two objectives for all the effective combinations, decision-makers may choose an appropriate one to control the disease. [ABSTRACT FROM AUTHOR]

Many discrete systems have more distinctive dynamical behaviors compared to continuous ones, which has led lots of researchers to investigate them. The discrete predator–prey model with two different functional responses (Holling type I and II functional responses) is discussed in this paper, which depicts a complex population relationship. The local dynamical behaviors of the interior fixed point of this system are studied. The detailed analysis reveals this system undergoes flip bifurcation and Neimark–Sacker bifurcation. Especially, we prove the existence of Marotto's chaos by analytical method. In addition, the hybrid control method is applied to control the chaos of this system. Numerical simulations are presented to support our research and demonstrate new dynamical behaviors, such as period-10, 19, 29, 39, 48 orbits and chaos in the sense of Li–Yorke. [ABSTRACT FROM AUTHOR]

This paper analyzes an allelopathic phytoplankton competition model, which was proposed by Bandyopadhyay [Dynamical analysis of a allelopathic phytoplankton model, J Biol Syst14(02):205–217, 2006]. Our study refines the previous results and finds at most three positive equilibria for the system. The existence conditions of all positive equilibria and the corresponding stability cases are given in the paper. Interesting dynamical phenomena such as bistability, saddle-node bifurcation, and cusp bifurcation are found. It is shown that the rate of toxin releases heavily influences the positive equilibria of the system under certain conditions. Numerical simulations verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, exact traveling wave solutions of space-time fractional simplified modified Camassa–Holm (mCH) equation are investigated by the bifurcation theory. The phase portraits of the equation are obtained with different parameter conditions. By analyzing different orbits, periodic wave, kink, anti-kink, burst wave, bright and dark solitary solutions of the equation are acquired. Finally, numerical simulation and the effects of fractional order taking on the dynamic behaviors of various forms of solutions are analytically discussed. [ABSTRACT FROM AUTHOR]

A power system shows chaotic oscillation when it is subjected to periodic load disturbance, which makes it a challenging and interesting problem for stability control of chaotic power system. In this paper, a unified controller is designed to solve the fixed-time and preassigned-time stability problems of fourth-order chaotic power systems. In addition, based on Lyapunov stability theory, sufficient conditions are established for the fixed-time and preassigned-time stability of the underlying chaotic power systems, and a more accurate estimation of the settling time is also derived. Finally, according to numerical simulations, we validate the theoretical results. [ABSTRACT FROM AUTHOR]

At present, stochastic resonance (SR) based on Duffing and Langevin equations has been widely studied, but there is little research on SR phenomenon in higher-dimensional fractional-order systems. Based on the fractional-order Lorenz-like system, the SR phenomenon is studied from the perspective of equilibrium point in this paper. The dynamic process of SR phenomenon is presented, and several key parameters are derived. The results of numerical simulation show that the boundary of SR and chaos system will be broken if the order of the fractional-order system or internal parameters is properly adjusted, and the effect of SR phenomenon will also be influenced. This paper connects two important nonlinear phenomena (chaos and SR) based on the fractional-order system, which provides a new idea for the conversion between chaos and SR systems. [ABSTRACT FROM AUTHOR]

This paper focuses on the dynamics of a submerged compound pendulum (SCP). The considered pendulum consists of a horizontal cylindrical element at its lowermost portion and a plate between the cylindrical element and the pivot. An approximate analytical expression for the natural frequency of the submerged compound pendulum is proposed. Further, a two-dimensional (2D) numerical model of the pendulum is developed using ANSYS (FLUENT). The natural periods of the SCP are determined for different geometric configurations. The analytically estimated natural periods of the pendulum match well with those obtained from numerical simulation. [ABSTRACT FROM AUTHOR]

The isolation technologies are adopted to protect the long-span space structures from serious damage under the action of earthquakes. When the isolation system is applied to the space structures, both horizontal and vertical vibration control effects on the structures should be concerned. In this paper, a two-dimensional earthquake isolation and mitigation device (TEIMD) composed of a high-damping viscoelastic (VE) core pad and VE dampers is proposed. Based on the dynamic shear experiment results of the VE damper, the energy dissipation capability of VE material is preferable. Then, the nonlinear equivalent stiffness and equivalent damping ratio of the TEIMD in horizontal and vertical directions are evaluated by using the numerical simulation method. The TEIMDs are arranged on the column top of a double-layer grid structure to assess the isolation effectiveness of the novel device. The dynamic analysis results of the double-layer grid structure with and without TEIMD reveal that this novel device can significantly reduce the acceleration response of the upper grid by relying on the strong energy dissipation performances in the horizontal and vertical directions. This research also verifies the feasibility of applying the TEIMD to the double-layer grid structure, which can effectively dissipate the vertical vibration energy of the structure. [ABSTRACT FROM AUTHOR]

This paper presents an innovative and efficient method for solving the fractional-order Van der Pol impulsive system. In particular, the proposed scheme utilizes finite difference techniques for approximating fractional integrals, and its efficacy is compared to existing integration methods presented in the literature. Moreover, the proposed approach is applied to fractional impulsive systems, specifically the Fractional Van der Pol system with impulse behavior. The results demonstrate the effectiveness of the impulsive treatment effects for the system under consideration. In general, this study offers an insightful contribution to the field of fractional calculus, while providing a practical and efficient solution for solving impulsive systems. [ABSTRACT FROM AUTHOR]

This paper describes the novel mathematical modeling of the 3-phase induction motor, various operations and study of its dynamic behavior and regenerative braking based on the model. This model uses v/f scheme to apply braking operation with the energy flow to the supply system instead of wasting the energy in braking resistor. It discusses the theory of induction motors, which is explored through both equations and computer simulation model using SIMULINK. The model also helps to study the behavior of the motor during its starting and load variation. The results from the analysis prove the demonstration of regenerative braking and the dynamic behavior and can give an opportunity to learn the different characteristics during these conditions. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a delayed diffusive predator–prey model affected by toxic substances. We first study the boundedness and persistence property of the model. By analyzing the associated characteristic equation, we obtain the conditions for the existence of steady state bifurcation, Hopf bifurcation and Turing bifurcation. Furthermore, we also study the Hopf bifurcation induced by the delay. Finally, our theoretical results are verified by numerical simulation. The numerical observation results are in good agreement with the theoretically predicted results. Theoretical and numerical simulations indicate that toxic substances have a great impact on the dynamics of the system. [ABSTRACT FROM AUTHOR]

The spread of infectious diseases often presents the emergent properties, which leads to more difficulties in prevention and treatment. In this paper, the SIR model with both delay and network is investigated to show the emergent properties of the infectious diseases' spread. The stability of the SIR model with a delay and two delay is analyzed to illustrate the effect of delay on the periodic outbreak of the epidemic. Then the stability conditions of Hopf bifurcation are derived by using central manifold to obtain the direction of bifurcation, which is vital for the generation of emergent behavior. Also, numerical simulation shows that the connection probability can affect the types of the spatio-temporal patterns, further induces the emergent properties. Finally, the emergent properties of COVID-19 are explained by the above results. [ABSTRACT FROM AUTHOR]

The study of rumor propagation dynamics is of great significance to reduce false news and ensure the authenticity of news information. In this paper, a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied. First, through stability analysis, we obtain the conditions for the existence and local stability of the positive equilibrium point. By selecting suitable variable as the control parameter, the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained. Then, using the above theorem and multi-scale standard analysis, the expression of amplitude equation around Turing bifurcation point is obtained. By analyzing the amplitude equation, different types of Turing pattern are divided such as uniform steady-state mode, hexagonal mode, stripe mode and mixed structure mode. Further, in the numerical simulation part, by observing different patterns corresponding to different values of control variable, the correctness of the theory is verified. Finally, the effects of different network structures on patterns are investigated. The results show that there are significant differences in the distribution of users on different network structures. [ABSTRACT FROM AUTHOR]

In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values x (0) , z (0) and u (0) of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the u -coordinate, which verifies the initial-offset boosting behavior of the system. Then the complex dynamical behavior of the system is studied in detail through the phase portraits of coexisting attractors, the average value of state variables, Lyapunov exponent spectrum, bifurcation diagram, attraction basin and the complexity of spectral entropy (SE). In addition, the simulation of the Multisim circuit is also carried out, and the results of numerical simulation and analog circuit simulation are consistent. Finally, the chaotic sequence generated by the system is applied to image encryption, and according to the performance analysis, the proposed chaotic system has good security performance. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear dynamical behaviors of a time-delayed supercavitating vehicle system varying with the system parameters, and proposes control strategies to stabilize the trajectory. A simplified dynamical model of the supercavitating vehicle is firstly constructed and then analyzed on its local and global stability in terms of different parameter values and initial conditions. Due to the forces resulting from the fins and the afterbody plane causing one of the system parameters to become a piecewise constant function of position, the system is described as a linear switched one with time delay. Both theoretical analysis and numerical simulations are adopted to describe the system behaviors. Several special phenomena such as bifurcations, deviation behaviors and period-doubling processes emerging from the system for a given set of parameters are discussed in detail in this paper. Besides, the equilibrium and chaotic solutions are accurately located by plotting the Lyapunov exponent map. Chaotic attractors present different strange forms with the variation of the parameters. Finally, based on the system's global property, the control and anti-control strategies are proposed to stabilize the system or generate desirable chaos and it is shown that the system can be controlled by selecting appropriate control parameters. [ABSTRACT FROM AUTHOR]

With the ongoing development and deployment of medium-low speed maglev vehicles in China, it has become common to increase operational speeds from 100 km/h up to 140 km/h or even 160 km/h, necessitating further studies and simulation models to understand the implications of these changes. This paper analyzes medium-speed maglev vehicle-track-girder coupling dynamic performance at a speed of 160 km/h. First, a field dynamics experiment is carried out on the Changsha Maglev Express with a running speed of 80–140 km/h. Then we introduce the distributed coupling simulation platform for maglev transportation system (MTS-DCSP) and the vehicle-track-girder coupling model, taking into account the complex vehicle structure, the guideway structure, and the Proportion Integral Differential (PID) levitation control system. Together, this platform and model can conduct a simulation of the complete process at scale and at all degrees of freedom to obtain accurate results. Our analysis of the results gives an accurate portrayal of the coupling dynamics properties and validates the coupling model. The results from the field experiments together with the coupling simulation demonstrate that the medium-speed maglev train can operate safely and stably within the range of 140–160 km/h. While at 140 km/h, however, the Sperling ride quality index (RQI) is about 2.5, which is within the Excellent grade range, at a speed of 160 km/h, the Sperling ride quality index can increase to as high as 2.74, which is a grade of Good. Therefore, it is necessary to optimize the parameters of the secondary suspension system to improve the ride comfort of the maglev vehicle at 160 km/h. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spatiotemporal dynamics of the Sel'kov–Schnakenberg system. The stability of the positive constant steady state is studied by the linear stability theory. Hopf bifurcation and Turing–Hopf bifurcation are generated by varying two parameters in the model. The normal form near the Turing–Hopf singularity is calculated to explore the complex dynamics of the system. Finally, numerical simulations are carried out to verify the theoretical results. Our results show that the Sel'kov–Schnakenberg system exhibits complex dynamics near the Turing–Hopf singularity, including the existence of inhomogeneous steady states, homogeneous periodic solutions and inhomogeneous periodic solutions. [ABSTRACT FROM AUTHOR]

The fractional derivative holds historical dependence or memory effects. But it also brings error accumulation of the numerical solutions as well as the theoretical analysis since many properties from the integer order case cannot hold. The fractional difference is discrete counterpart of the fractional derivative. The memory kernel is defined by applying the discrete functions on time scale and avoids the errors from the numerical discretization. It is particularly suitable for fractional modeling with computer implementations. Many applications of fractional dynamics to neural networks, signal processing, time series and big data become possible now. This issue of work presents the latest progress in the neighborhood related to fractional calculus. [ABSTRACT FROM AUTHOR]

The operator-splitting (OS) method for real-time substructure testing (RTST) provides explicit and unconditionally stable solutions for structures with softening type stiffness and damping has been widely used for precisely disclosing the seismic performance of structures with velocity-dependent specimens. However, the OS method for RTST provides only explicit target displacement and velocity but not an explicit target acceleration, so that it is essentially an implicit method for Dynamic real-time substructure testing (DRTST) with dynamic system specimens. For precisely disclosing the seismic performance of multiple-degree-of-freedom structures with dynamic system specimens, one improved OS method is proposed for DRTST in this paper. The methodology and stability of the proposed OS method are investigated, and the effectiveness of the proposed OS method is validated by numerical simulations and experimental tests. By using the predictor displacement, velocity, and acceleration approximations, the OS method is an explicit algorithm for DRTST. The stability analysis shows that the proposed OS method is conditionally stable for DRTST, and its stability limit decreases with the increase of the mass ratio and the stiffness ratio, while it increases first and then decreases with the increase of the damping ratio. The numerical and experimental results confirm the stability and accuracy of the OS method. The OS method for DRTST provides a practical and precise investigation strategy for structures with dynamic system specimens and may have broad application prospects in civil engineering. [ABSTRACT FROM AUTHOR]

The micromixer is an important prerequisite for realizing the function of the microfluidic chip system. Micromixers are mainly used in protein crystallization, biological reactions, drug delivery and other fields. Efficient micromixers enable fast bioreaction processes. In this paper, according to the principle of plane geometry, micromixers with three different structural obstacles, circular, equilateral triangle and square, are designed to study how to improve the mixing efficiency of the micromixer. In this paper, the influence of the obstacle structure on the mixing efficiency and pressure drop of the micromixer is analyzed. Through numerical simulation, the results show that when Re = 100, the mixing efficiency of the circular obstacle micromixer is up to 97.4%, and the pressure drop is 15,789.597 Pa. In addition, this paper analyzes that the use of cylindrical obstacles can make the fluid generate horizontal and vertical vortex flow, break the usual laminar flow, and significantly improve the mixing efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a new three-dimensional chaotic system with two exponential nonlinearities is presented. The analysis of fixed points of the proposed system suggests existence of one hyperbolic index-2 spiral saddle-type fixed point. The proposed system fulfils Shilnikov criterion and nature of the chaos is found to be dissipative. Bifurcation diagrams, maximum Lyapunov exponents and Kaplan–Yorke dimension are examined through numerical simulations to investigate dynamics of proposed system. The hardware feasibility of the proposed system is illustrated through current feedback operational amplifier (CFOA)-based circuit implementation. The proposed circuit uses six CFOAs, two diodes to establish nonlinearity, eleven resistors and three capacitors. The absence of analog multiplier in the proposed circuit makes it superior to the existing counterpart in the sense that it does not require area and power-consuming active building block. To confirm the chaotic nature of the proposed circuit, LTspice simulations are done to obtain phase portraits which are found to be strange attractors and are topologically different from the shape of the existing attractors. Moreover, we have investigated the synchronization of the proposed chaotic system using adaptive control scheme and proposed CFOA-based complete circuit design of the adaptively synchronized system. Also, the effect of the tolerance of passive components and temperature on the behavior of the proposed chaotic circuit and the complete synchronization circuit has also been studied. It is found that the circuit is sensitive to the value of resistors and temperature to an extent and can work properly within their limits. [ABSTRACT FROM AUTHOR]

Micro-Electro-Mechanical System (MEMS)-based pressure sensors operating on the principle of piezoresistivity have found profound application in various fields like automobile, aerospace, aviation, biomedical and consumer electronics. Various research studies have been conducted to optimize the design of MEMS-based pressure sensors to meet specific requirements of different fields. Modification in the structure of the piezoresistors placed on these sensors has shown great effect in this regard. However, most of these improvements have been validated through fabrication and measurement, but there has been a lack of significant studies developing analytical models to explain these improvements. This paper studies the performance of a single-turn piezoresistor design on a square silicon diaphragm. The analytical model relates the dimensions of the single-turn piezoresistor on a square diaphragm to the output voltage, and hence, sensor sensitivity is laid out. The correctness of the relation is also validated through Finite Element Analysis (FEA) performed using COMSOL Multiphysics software. Hence, an optimized single-turn design is presented which achieves a sensitivity of 203.57 mV/V/MPa over a pressure range of 0–1 MPa. These results are then compared to work from existing literature. The comparison shows an improved performance which was achieved by optimizing the design through its derived analytical model. The proposed sensor can be utilized in disposable blood pressure measurement system where high sensor sensitivity is required. [ABSTRACT FROM AUTHOR]

This paper concerns the issue of fixed-time synchronization (FXTS) for complex networks composed of dynamical nodes with discontinuous dynamics, abbreviated as discontinuous dynamic networks, under the concept of Filippov solution. In terms of 1 -norm and 2 -norm, two types of simple control schemes without the linear feedback part are, respectively, designed to compel the considered discontinuous dynamic network to fixed-timely synchronize with a desired trajectory. By utilizing a novel two-stage analysis approach, some new FXTS criteria are derived. Compared with the existing research works, the established theoretical results not only are more relaxed, but also improve the estimation accuracy of synchronous settling time. Finally, the validity of the analytical results is verified via numerical simulations. [ABSTRACT FROM AUTHOR]

Optimal control technique is crucial to improve the yield of microbial fermentation production. In this paper, we propose a nonlinear control system with state-dependent impulses, where the impulsive volume of feeding glycerol and the critical concentration of glycerol for occurring impulse are the control variables, to formulate 1,3-propanediol (1,3-PD) fed-batch production process. We also discuss a quantity of important properties for this control system. Then, we analyze the sensitivity of system state with respect to the kinetic parameters. We further propose a constrained optimal control model governed by the control system with state-dependent impulses. The existence of the optimal impulsive controls is established. For solving this problem, we utilize an exact penalty method to transform the problem into an optimization problem with only box constraints. Moreover, an improved differential evolution method is developed to seek the optimal impulsive strategy. Finally, numerical simulation results demonstrate that, by using the optimal impulsive strategies, final 1,3-PD concentration is considerably increased under the nominal parameter values and disturbances of kinetic parameters have significant effects on the optimal final 1,3-PD yield. [ABSTRACT FROM AUTHOR]

The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we apply the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the second-order scalar auxiliary variable approach combined with finite difference method is employed for the Allen–Cahn equation that represents a phenomenological model for antiphase domain coarsening in a binary mixture. The second-order backward differentiation formula is used in time. The error estimation of the semi-discrete scheme is derived in the sense of L 2 -norm. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a new mosquito population suppression model with stage and sex structure is constructed, which is composed of two sub-models switching each other. Sterile mosquitoes are released with period T and remain sexually active for time T ̄. For the case T ̄ < T , three thresholds T * , m * and c * are determined for the release period T and release amount c. According to the values of T and c in different ranges determined by these thresholds, we study the dynamical behavior of the system for different release strategies, mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions. Finally, some numerical simulations are performed to illustrate our results. [ABSTRACT FROM AUTHOR]

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper. By using Lyapunov methods and Itô formula, we first prove that the system has a unique global positive solution with any positive initial value. Then combining inequality technique and the ergodic property of Markov switching, the sufficient conditions for extinction and persistence in the mean of the disease are established. The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state. Meanwhile, the high incidence rate will slow down the extinction of the disease. Specially, the switching noise can induce the system to toggle between the extinct and persistent states. Finally, some numerical simulations are carried out to confirm the analytical results. [ABSTRACT FROM AUTHOR]

This paper proposes a diffusive predator–prey model with Allee effect, time delay and anti-predator behavior. First, the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied. Using the normal form and center manifold theory, the formulas which can determine the direction, period and stability of Hopf bifurcation are obtained. Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations, and anti-predator behavior can greatly improve the stability of the coexisting equilibrium. [ABSTRACT FROM AUTHOR]

In this paper, we study a commensal model with Allee effect and herd behavior. Firstly, the stability of all possible equilibria are investigated. Secondly, using the Sotomayor's theorem, we prove the existence of saddle-node bifurcation and pitchfork bifurcation. Finally, all the theoretical predictions on the bifurcation are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

By introducing new variables in the systems of difference equations from the paper [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contrib. Sec. Math. Tech. Sci. 33 (2012) 75–96], new systems of difference equations are obtained. The solutions of these new systems of difference equations depend only on the initial values a 0 , b 0 , c 0 and the coefficients a i , i ∈ N. The power series whose coefficients are these solutions present the recurrent solutions for the Lorenz system of differential equations. A comparison between the behavior of the Lorenz system of differential equations and the local behavior of its recurrent solutions for small time steps is examined in examples by computer simulations, as in the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contrib. Sec. Math. Tech. Sci. 33 (2012) 75–96; B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. Fifth Int. Scientific Conf. FMNS - 2013, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107 and B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (2017) 51–61]. [ABSTRACT FROM AUTHOR]

Cellular automaton (CA) as a discrete and deterministic dynamic system has been widely used in cryptography. In this paper, a novel triple-coupling CA model is proposed. We first apply the triple-coupling model to 1D CA to design a high-quality pseudo-random number generator (PRNG). Numerical simulation and analyses show that triple-coupling CA exhibits more complex evolutionary behavior than uncoupling CA. The pseudo-random sequence generated by triple-coupling 1D CA can pass all NIST SP800-22 tests. Subsequently, the triple-coupling model is also applied to 2D CA, and a novel image encryption scheme based on this model is proposed. Thanks to the triple-coupling model, the diffusion operation can be completed between different color channels of the color image. Experimental simulations and extensive cryptanalysis show that the image encryption algorithm using the triple-coupling model has superior security and high efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a size-structured population model is studied. Choosing the coefficient of birth function as the varying parameter, we prove the existence of Hopf bifurcation and discuss the bifurcation properties, such as the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. The methods used in this paper include Hopf bifurcation theorem, center manifold theorem and normal form theory for the abstract Cauchy problems in a nondense domain. Numerical simulations are finally carried out to show the theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims to improve the performance of the piezoelectric buckled beam under low vibration environment using the noncontact magnetic modulation method. Based on the bi-stable buckling beam structure, the magnetic force is introduced to capture more energy. In order to investigate the influence of magnetic force in the process of vibration, the dynamic response of the harvester is analyzed under different magnetic force through numerical simulation and experiment. It is found that the magnetic force has a softening effect on the structure, namely, it could reduce the stiffness of the buckled beam. Therefore, the energy harvester could realize large-amplitude vibration under low-amplitude or low-frequency vibration with the help of magnetic force. The experimental results show that the harvester can realize inter-well vibration only when the vibration acceleration is 3.5 g and the frequency is 15 Hz without the magnetic force. The harvester only needs 2.5 g acceleration or 10 Hz vibration frequency to realize the large-amplitude vibration. While in the case of 12 mm magnetic gap. After the magnetic force is introduced in the harvester, the voltage output under 2.5 g acceleration is increased from 1 to 4 V, and the voltage output at 10 Hz vibration frequency is increased from 0.2 to 2 V. Therefore, the proposed magnetically tuned bi-stable energy harvester can better operate in low frequency and low amplitude environments. [ABSTRACT FROM AUTHOR]

Lag synchronization is a special synchronization manner and has wide applications. For community network, in view of the differences among communities, the synchronization lags in different communities may be nonidentical. This paper investigates the cluster lag synchronization in fractional-order community networks with nondelay and delay coupling. The node dynamics in different communities are nonidentical and even have nonidentical dimensions. Based on the Lyapunov stability theory, effective feedback controllers are designed for achieving cluster lag synchronization and several synchronization criteria are derived. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

A stochastic susceptible–infected–recovered–infected (SIRI) epidemic model with relapse and reinfection is established in this paper. First, we prove that the solution to the epidemic model is unique and globally positive. Next, we determine some sufficient conditions for the extinction of the disease when ℛ0s < 1 and for the persistence in mean in the case of ℛ0s̄ > 1. Furthermore, we prove the existence of at least one ergodic stationary distribution of the stochastic model if ℛ0s̄ > 1. Additionally, by solving the corresponding three-dimensional Fokker–Planck equation, it is theoretically shown that the epidemic model has a log-normal probability density function when ℛ0s̄ > 1, then we obtain the exact expression of density function of the stationary distribution. Finally, we give some numerical simulations to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a two-patch model with additive Allee effect, nonlinear dispersal and commensalism is proposed and studied. The stability of equilibria and the existence of saddle-node bifurcation, transcritical bifurcation are discussed. Through qualitative analysis of the model, we know that the persistence and the extinction of population are influenced by the Allee effect, dispersal and commensalism. Combining with numerical simulation, the study shows that the total population density will increase when the Allee effect constant a increases or m decreases. In addition to suppress the Allee effect, nonlinear dispersal and commensalism are crucial to the survival of the species in the two patches. [ABSTRACT FROM AUTHOR]

The cognitive abilities of animals, such as memory, have a significant impact on their movement in space. In this paper, we consider a radio-dependent model with memory-based diffusion under the conditions of Neumann boundary. The stability of a positive equilibrium and the existence of the Turing–Hopf bifurcation induced by memory diffusion and memory delay are carried out in details. Notably, our findings indicate that with a relatively short average memory period, the large memory diffusion can stabilize an otherwise unstable equilibrium. In addition, the third-order truncated normal form for the Turing–Hopf bifurcation restricted to the central manifold is derived, which can reveal the generation of some steady-state and time-periodic solutions with spatial heterogeneity. The coefficients within the normal form are systematically determined through matrix operations, and these results can also be applied to other models with memory diffusion. Ultimately, leveraging the theoretical findings, we elucidated the intricate spatial-temporal dynamics and their associated parameter scopes caused by Turing–Hopf bifurcation through numerical simulations. [ABSTRACT FROM AUTHOR]