27 results on '"uniform persistence"'
Search Results
2. Dynamical analysis of a reaction–diffusion mosquito-borne model in a spatially heterogeneous environment
- Author
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Wang Jinliang, Wu Wenjing, and Li Chunyang
- Subjects
mosquito-borne disease model ,basic reproduction number ,spatial heterogeneity ,uniform persistence ,lyapunov function ,35k57 ,35j57 ,35b40 ,92d25 ,Analysis ,QA299.6-433 - Abstract
In this article, we formulate and perform a strict analysis of a reaction–diffusion mosquito-borne disease model with total human populations stabilizing at H(x) in a spatially heterogeneous environment. By utilizing some fundamental theories of the dynamical system, we establish the threshold-type results of the model relying on the basic reproduction number. Specifically, we explore the mutual impacts of the spatial heterogeneity and diffusion coefficients on the basic reproduction number and investigate the existence, uniqueness, and global attractivity of the nontrivial steady state by utilizing the arguments of asymptotically autonomous semiflows. For the case that all parameters are independent of space, the global attractivity of the nontrivial steady state is achieved by the Lyapunov function. more...
- Published
- 2023
- Full Text
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3. Dynamics of a Predator–Prey Model with Distributed Delay to Represent the Conversion Process or Maturation.
- Author
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Teslya, Alexandra and Wolkowicz, Gail S. K.
- Abstract
Distributed delay is included in a simple predator–prey model in the prey-to-predator biomass conversion term. The delayed term includes a delay-dependent "discount" factor that ensures the predators that do not survive the delay interval, do not contribute to growth of the predator population. A simple model was chosen so that without delay all solutions converge to a globally asymptotically stable equilibrium in order to show the possible effects of delay on the dynamics. If the co-existence equilibrium does not exist, the dynamics of the system is identical to its non-delayed analog. However, with delay, there is a delay-dependent threshold for the existence of the co-existence equilibrium. When the co-existence equilibrium exists, unlike the dynamics of the model without delay, a much wider range of dynamics is possible, including a strange attractor and bi-stability, although the system is uniformly persistent. A bifurcation theory approach is taken, using both the mean delay and the predator death rate as bifurcation parameters. We consider the gamma and the uniform distributions as delay kernels and show that the "discounting" term ensures that the Hopf bifurcations occur in pairs, as was observed in the analogous system with discrete delay (i.e., using the Dirac delta distribution). We show that there are certain features common to all distributions, although the model with different kernels can have a significantly different range of dynamics. In particular, the number of bi-stabilities, the sequence of bifurcations, the criticality of the Hopf bifurcations, and the size of the stability regions can differ. Also, the width of the interval over which the delay history is nonzero seems to have a significant effect on the range of dynamics. Thus, ignoring the delay and/or not choosing the right delay kernel might result in inaccurate modelling predictions. [ABSTRACT FROM AUTHOR] more...
- Published
- 2023
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4. Asymptotic profiles of a diffusive SIS epidemic model with vector-mediated infection and logistic source.
- Author
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Guo, Yutong, Wang, Jinliang, and Ji, Desheng
- Subjects
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BASIC reproduction number , *NEUMANN boundary conditions , *INFECTIOUS disease transmission , *EPIDEMICS , *LYAPUNOV functions - Abstract
In order to complement some clues for analytical pursuits and potential applications in disease control and prevention, we propose a diffusive susceptible-infective-susceptible (SIS) epidemic model incorporating a logistic growth source and a vector-mediated infection mechanism. Under the Neumann boundary condition and environmental heterogeneity, we carry out the qualitative analysis to achieve the basic reproduction number served as the threshold-type value of the model. Specifically, without environmental heterogeneity, the global attractivity of the unique constant endemic equilibrium is proved by Lyapunov function method. We further explore the asymptotic profiles of endemic equilibrium as the diffusion rates of humans approaching to zero or infinity. We find that the strategies that limiting and releasing the diffusion rates do not help eliminating disease in our current model since the steady state can stay above a positive level, which brings a useful insight in investigating the effects of the environmental heterogeneity and spatial diffusion on disease spread and control. [ABSTRACT FROM AUTHOR] more...
- Published
- 2022
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5. A Spatially Dependent Vaccination Model with Therapeutic Impact and Non-linear Incidence
- Author
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Mahmud, Md. Shahriar, Kamrujjaman, Md., Islam, Md. Shafiqul, Cavas-Martínez, Francisco, Series Editor, Chaari, Fakher, Series Editor, Gherardini, Francesco, Series Editor, Haddar, Mohamed, Series Editor, Ivanov, Vitalii, Series Editor, Kwon, Young W., Series Editor, Trojanowska, Justyna, Series Editor, Mishra, S. R., editor, Dhamala, T. N., editor, and Makinde, O. D., editor more...
- Published
- 2021
- Full Text
- View/download PDF
6. Permanence via invasion graphs: incorporating community assembly into modern coexistence theory.
- Author
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Hofbauer, Josef and Schreiber, Sebastian J.
- Abstract
To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all - i communities, i.e., communities without species i where all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence. [ABSTRACT FROM AUTHOR] more...
- Published
- 2022
- Full Text
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7. Global dynamics of a generalist predator–prey model in open advective environments.
- Author
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Lou, Yuan and Nie, Hua
- Abstract
This paper deals with a system of reaction–diffusion–advection equations for a generalist predator–prey model in open advective environments, subject to an unidirectional flow. In contrast to the specialist predator–prey model, the dynamics of this system is more complex. It turns out that there exist some critical advection rates and predation rates, which classify the global dynamics of the generalist predator–prey system into three or four scenarios: (1) coexistence; (2) persistence of prey only; (3) persistence of predators only; and (4) extinction of both species. Moreover, the results reveal significant differences between the specialist predator–prey system and the generalist predator–prey system, including the evolution of the critical predation rates with respect to the ratio of the flow speeds; the take-over of the generalist predator; and the reduction in parameter range for the persistence of prey species alone. These findings may have important biological implications on the invasion of generalist predators in open advective environments. [ABSTRACT FROM AUTHOR] more...
- Published
- 2022
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8. Asymptotic profiles of a diffusive SIRS epidemic model with standard incidence mechanism and a logistic source.
- Author
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Pan, Yifei, Zhu, Siyao, and Wang, Jinliang
- Abstract
The asymptotic profiles of the endemic equilibrium play an important role in determining whether or not eliminating the infectious disease when considering the dispersal rates of populations approach to zero or infinity. This paper aims to provide a qualitative analysis of a reaction–diffusion Susceptible–Infective–Recovered–Susceptible epidemic model with standard incidence mechanism and a logistic source in a spatially heterogeneous environment. For this purpose, we first estimate the uniform bounds of the solution of the model. By the theory of uniform persistence, we explore the threshold-type result of the model in terms of the basic reproduction number ℜ 0 . Compared to the results in Han et al. (Z Angew Math Phys 71:190, 2020) where the growth of susceptible population is adopt by linear source, our theoretical results reveal that controlling the dispersal rates of population cannot eradicate the disease, and the infection component of the steady state solution approaches to nonzero level when the dispersal rates of populations approach to zero or infinity. We also obtain that varying total population enhances persistence of infectious disease, the results are consistent with Li et al. (Z Angew Math Phys 68:96, 2017). [ABSTRACT FROM AUTHOR] more...
- Published
- 2022
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9. Analysis of a reaction–diffusion SVIR model with a fixed latent period and non-local infections.
- Author
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Gao, Jianguo, Zhang, Chao, and Wang, Jinliang
- Subjects
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BASIC reproduction number , *HUMAN mechanics , *INFECTIOUS disease transmission , *REPRODUCTION - Abstract
This paper concerns with a reaction–diffusion susceptible-vaccinated-infectious-recovered model with a fixed latent period. The model is formulated as a non-local and time-delayed reaction–diffusion model due to the fact that an individual infected by the disease in one place may not stay at the same space in the domain due to the movement of human during the incubation period. We then derive the basic reproduction number ℜ 0 as the spectral radius of the next infection operator and show that it serves as a threshold role in predicting whether the disease will spread. Further, the explicit formula of basic reproduction number is obtained when all model parameters to be positive constants and the domain to the one-dimensional case. Moreover, we demonstrate the differences in the form of basic reproduction number between the standard incidence and bilinear incidence rate. [ABSTRACT FROM AUTHOR] more...
- Published
- 2022
- Full Text
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10. Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology.
- Author
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Kamrujjaman, Md., Shahriar Mahmud, Md., and Islam, Md. Shafiqul
- Subjects
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VACCINATION , *BASIC reproduction number , *FINITE differences , *COMMUNICABLE diseases , *EPIDEMIOLOGY - Abstract
In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of R n with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level R 0 ≤ 1 , the disease-free equilibrium E 0 is globally asymptotically stable. On the other hand, if R 0 > 1 then there exists a unique stable disease equilibrium E ∗ . The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value R 0 . [ABSTRACT FROM AUTHOR] more...
- Published
- 2021
- Full Text
- View/download PDF
11. Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model.
- Author
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Zhou, Hui, Alzabut, Jehad, Rezapour, Shahram, and Samei, Mohammad Esmael
- Subjects
- *
GLOBAL asymptotic stability , *LYAPUNOV functions , *GLOBAL analysis (Mathematics) , *DIFFERENTIAL inequalities ,PERSISTENCE - Abstract
In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes. [ABSTRACT FROM AUTHOR] more...
- Published
- 2020
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12. Period-doubling and Neimark–Sacker bifurcations in a larch budmoth population model.
- Author
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De Silva, T. Mihiri M. and Jang, Sophia R.-J.
- Subjects
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ZEIRAPHERA diniana , *BIFURCATION theory , *MATHEMATICAL models - Abstract
We investigate a discrete consumer-resource system based on a model originally proposed for studying the cyclic dynamics of the larch budmoth population in the Swiss Alps. It is shown that the moth population can persist indefinitely for all of the biologically feasible parameter values. Using intrinsic growth rate of the consumer population as a bifurcation parameter, we prove that the system can either undergo a period-doubling or a Neimark–Sacker bifurcation when the unique interior steady state loses its stability. [ABSTRACT FROM AUTHOR] more...
- Published
- 2017
- Full Text
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13. Permanence via invasion graphs: Incorporating community assembly into Modern Coexistence Theory
- Author
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Josef Hofbauer and Sebastian J. Schreiber
- Subjects
Life on Land ,Bioinformatics ,Quantitative Biology::Tissues and Organs ,Population Dynamics ,Dynamical Systems (math.DS) ,92D25 ,Models, Biological ,Mathematical Sciences ,Models ,FOS: Mathematics ,Quantitative Biology::Populations and Evolution ,Mathematics - Dynamical Systems ,Quantitative Biology - Populations and Evolution ,Uniform persistence ,Ecosystem ,Community assembly ,Applied Mathematics ,Lyapunov exponents ,Populations and Evolution (q-bio.PE) ,Biological Sciences ,Biological ,Agricultural and Biological Sciences (miscellaneous) ,Permanence ,Modeling and Simulation ,FOS: Biological sciences ,Coexistence - Abstract
To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all $$-i$$ - i communities, i.e., communities without species i where all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence. more...
- Published
- 2022
14. Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis.
- Author
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Wu, Sainan, Shi, Junping, and Wu, Boying
- Subjects
- *
EXISTENCE theorems , *LOTKA-Volterra equations , *MATHEMATICAL proofs , *MATHEMATICAL bounds , *NUMERICAL solutions to reaction-diffusion equations , *COEFFICIENTS (Statistics) - Abstract
This paper proves the global existence and boundedness of solutions to a general reaction–diffusion predator–prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence of the system under some additional conditions. Applications to models from ecology and chemotaxis are discussed. [ABSTRACT FROM AUTHOR] more...
- Published
- 2016
- Full Text
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15. Deterministic and stochastic nutrient-phytoplankton- zooplankton models with periodic toxin producing phytoplankton.
- Author
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Jang, Sophia R.-J. and Allen, Edward J.
- Subjects
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STOCHASTIC models , *PLANT nutrients , *PHYTOPLANKTON populations , *ZOOPLANKTON , *PLANT toxins - Abstract
Deterministic and stochastic models of nutrient-phytoplankton-zooplankton interaction are proposed to investigate the impact of toxin producing phytoplankton upon persistence of the populations. The toxin liberation by phytoplankton is modeled periodically in the deterministic system. We derive two thresholds in terms of the parameters for which both plankton populations can persist if these thresholds are positive. We construct stochastic models with Itô differential equations to model variability in the environment. It is concluded that the input nutrient concentration along with the toxin liberation rate play critical roles in the dynamics of the planktonic interaction. In particular, toxin producing phytoplankton can terminate harmful algal blooms and the planktonic interaction is more stable if either the input nutrient concentration is smaller or if the toxin production rate is larger. [ABSTRACT FROM AUTHOR] more...
- Published
- 2015
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16. A pivotal eigenvalue problem in river ecology.
- Author
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Hsu, Sze-Bi, López-Gómez, Julián, Mei, Linfeng, and Wang, Feng-Bin
- Subjects
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EIGENVALUES , *RIVER ecology , *EXISTENCE theorems , *PARABOLIC differential equations , *UNIQUENESS (Mathematics) , *MATHEMATICAL models - Abstract
This paper studies an eigenvalue problem associated with a linear parabolic equation and a coupled ordinary differential equation. The existence and the uniqueness of the principal eigenvalue for this eigenvalue problem is first established. Then, the qualitative dependence of the principal eigenvalue with respect to the several parameters involved in the system is analyzed. Finally, these results are applied to a system in flowing habitats with a hydraulic storage zone and light limitation. [ABSTRACT FROM AUTHOR] more...
- Published
- 2015
- Full Text
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17. A permanence theorem for local dynamical systems.
- Author
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Fonda, Alessandro and Gidoni, Paolo
- Subjects
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LOTKA-Volterra equations , *BIOLOGICAL mathematical modeling , *NONLINEAR differential equations , *MATHEMATICAL functions , *MATHEMATICAL analysis - Abstract
We provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition. [ABSTRACT FROM AUTHOR] more...
- Published
- 2015
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18. Discrete-time host–parasitoid models with pest control.
- Author
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Jang, SophiaR.-J. and Yu, Jui-Ling
- Subjects
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PEST control , *DISCRETE-time systems , *PHYSIOLOGICAL control systems , *HOPF bifurcations , *OPTIMAL control theory , *PONTRYAGIN'S minimum principle ,HOSTS of parasitoids - Abstract
We propose a simple discrete-time host–parasitoid model to investigate the impact of external input of parasitoids upon the host–parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host–parasitoid dynamics when the host population practices contest competition. We then consider a corresponding optimal control problem over a finite time period. We also derive an optimal control model using a chemical as a control for the hosts. Applying the forward–backward sweep method, we solve the optimal control problems numerically and compare the optimal host populations with the host populations when no control is applied. Our study concludes that applying a chemical to eliminate the hosts directly may be a more effective control strategy than using the parasitoids to indirectly suppress the hosts. [ABSTRACT FROM PUBLISHER] more...
- Published
- 2012
- Full Text
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19. Cannibalism in discrete-time predator–prey systems.
- Author
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Chow, Yunshyong and Jang, SophiaR.-J.
- Subjects
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CANNIBALISM , *POPULATION biology , *DISCRETE-time systems , *PREDATION , *COMPUTER simulation , *PARAMETER estimation , *MATHEMATICAL models - Abstract
In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population. Based on this model, we study two systems of predator–prey interactions where the prey population is cannibalistic. A sufficient condition based on the nontrivial boundary steady state for which both populations can coexist is derived. It is found via numerical simulations that introduction of the predator population may either stabilize or destabilize the prey dynamics, depending on cannibalism coefficients and other vital parameters. [ABSTRACT FROM PUBLISHER] more...
- Published
- 2012
- Full Text
- View/download PDF
20. Persistence and global stability in a selection-mutation size-structured model.
- Author
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Ackleh, AzmyS., Ma, Baoling, and Salceanu, PaulL.
- Subjects
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LYAPUNOV stability , *GENETIC mutation , *COMPETITION (Biology) , *MATHEMATICAL models , *ASYMPTOTIC expansions , *PERTURBATION theory - Abstract
We analyse a selection-mutation size-structured model with n ecotypes competing for common resources. Uniform persistence and robust uniform persistence are established, when the selection-mutation matrix Γ is irreducible, i.e. individuals of one ecotype may contribute directly or indirectly to individuals of other ecotypes. Similar results are also presented for a particular reducible form of Γ. In the case of pure selection in which the offspring of one ecotype belong to the same ecotype, i.e. Γ=I, the identity matrix, we prove that the boundary equilibrium that describes competitive exclusion, with the fittest being the winner ecotype, is globally asymptotically stable. We show that small perturbations of the pure selection matrix lead to the existence of globally asymptotically stable interior equilibria. For the case when the selection-mutation matrix is reducible, we present and discuss the outcome of a series of numerical simulations. [ABSTRACT FROM AUTHOR] more...
- Published
- 2011
- Full Text
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21. Dynamics of a discrete-time host-parasitoid system with cannibalism.
- Author
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Jang, SophiaR.-J. and Yu, Jui-Ling
- Subjects
- *
HOST-parasite relationships , *POPULATION biology , *PARASITOIDS , *COMPUTER simulation , *DISCRETE-time systems , *BIFURCATION theory , *REPRODUCTION ,HOSTS of parasitoids - Abstract
A discrete-time, two-stage host population model in which adults may consume their offspring is proposed and analysed. It is shown that the population is stabilized at the unique interior equilibrium if the basic reproductive number of the population is larger than one and the population is not cannibalistic. If the mechanism of cannibalism is incorporated, then the model undergoes a discrete Hopf (Neimark-Sacker) bifurcation when the interior equilibrium loses its stability. We also study a system of host-parasitoid interaction based on the two-stage host population model. Numerical simulations suggest that the introduction of parasitoid may stabilize the system when the host population is oscillating in the absence of parasitoid. [ABSTRACT FROM AUTHOR] more...
- Published
- 2011
- Full Text
- View/download PDF
22. Uniform persistence for nonautonomous and random parabolic Kolmogorov systems
- Author
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Mierczyński, Janusz, Shen, Wenxian, and Zhao, Xiao-Qiang
- Subjects
- *
DIVISION rings , *LYAPUNOV exponents , *DIFFERENTIAL equations , *INVARIANT sets , *DIFFERENTIABLE dynamical systems - Abstract
The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in
n -species, particularly 3-species, random competitive systems. [Copyright &y& Elsevier] more...- Published
- 2004
- Full Text
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23. A spatiotemporal model of drug resistance in bacteria with mutations
- Author
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Hsu, Sze-Bi and Jiang, Jifa
- Subjects
37C65 ,35K57 ,35B40 ,competitive exclusion ,strong maximum principle ,uniform persistence ,invariance principle ,Lyapunov functional ,92D25 ,drug- resistance mutations - Abstract
A spatio-temporal dynamics model is presented to study the effects of mutations on the persistence and extinction of bacteria under the antibiotic inhibition. We construct a mixed type Lyapunov functional to prove the global stability of extinction state and coexistence state for the case of forward mutation and forward-backward mutation respectively. more...
- Published
- 2020
- Full Text
- View/download PDF
24. Persistence and stability in a ratio-dependent food-chain system with time delays
- Author
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Xu Rui, Feng Hanying, Yang Pinghua, and Wang Zhiqiang
- Published
- 2002
- Full Text
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25. Existence of Stable Periodic Orbits for a Predatory-Prey Model with Deddington-DeAngelis Functional Response and Delay
- Author
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Duque, C.
- Subjects
stable periodic orbit ,delay ,34K13 ,Quantitative Biology::Populations and Evolution ,Beddington-DeAngelis functional response ,predator-prey system ,uniform persistence ,92D25 - Abstract
In this paper a Beddington-DeAngelis predator-prey model with time lag for predator is proposed and analyzed. Mathematical analysis regard to boundedness of solutions, nature of equilibria, uniform persistence, and stability are analyzed. We show that if the positive equilibrium is unstable, an orbitally asymptotically stable periodic solution exists. more...
- Published
- 2014
26. Uniform persistence and net functions
- Author
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Cao, Yulin and Gard, Thomas C.
- Published
- 1995
- Full Text
- View/download PDF
27. Cannibalism in a discrete predator-prey model with an age structure in the prey
- Author
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Sophia R. Jang
- Subjects
Age structure ,inherent net reproductive number ,Cannibalism ,behavior and behavior mechanisms ,Zoology ,Liapunov-Schmidt expansion ,uniform persistence ,Biology ,92D25 ,Predation - Abstract
A discrete-time predator-prey model with an age structure in the prey population in which both the predator and the adult prey can consume juvenile prey population is proposed. The fecundity of the adult prey population is assumed to be a constant and the juvenile survival probability is density dependent on its own population size. It is shown that both populations go to extinction if the inherent net reproductive number of the prey is less than 1. Both populations can survive if the prey's inherent net reproductive number is larger than one and the predator's reproductive number is greater than 1 when the prey population is stabilized in the steady state fashion. more...
- Published
- 2009
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