RANDOM DISPERSAL IN A PREDATOR-PREY-PARASITE SYSTEM

2010 ◽  
Vol 18 (04) ◽  
pp. 825-845 ◽  
Author(s):  
SOPHIA R.-J. JANG ◽  
JAMES BAGLAMA ◽  
LI WU
Keyword(s):  
Steady State ◽  
Dynamical Behavior ◽  
Homogeneous System ◽  
Reproductive Number ◽  
Predator Prey ◽  
Random Dispersal ◽  
Prey Interaction ◽  
Asymptotic Dynamics ◽  
Two Parameters ◽  
Infected Prey

We propose predator-prey-parasite models to study the effects of parasites upon the predator-prey interaction. There are two parameters that are used to model the effectiveness of the infected prey and infected predator. For the spatial homogeneous system, the asymptotic dynamics depend on the reproductive number of the parasite. The parasite can persist in the population if this reproductive number is larger than one. Numerical simulations suggest that less competitiveness of the infected predator can make the predator-prey interaction less stable. The dynamics may move from coexisting steady state to oscillations. For the spatial heterogeneous system, diffusion may destabilize the homogeneous interior steady state for a particular set of diffusion coefficients. However, both systems do not exhibit complicated dynamical behavior.

SPATIOTEMPORAL DYNAMICS OF AN ECOEPIDEMIOLOGICAL MODEL WITH STANDARD INCIDENCE

2007 ◽  
Vol 07 (02) ◽  
pp. 175-197
Author(s):  
BANIBRATA MUKHOPADHYAY ◽  
R. BHATTACHARYYA
Keyword(s):  
Traveling Wave ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Homogeneous System ◽  
Viral Disease ◽  
Prey Population ◽  
Predator Species ◽  
Predator Prey ◽  
Prey Interaction ◽  
Bifurcation Behavior

We analyze a mathematical model of predator–prey interaction where the prey population is infected with a viral disease. Infection in the prey population is assumed to follow standard incidence. The dynamical behavior of the system is studied in terms of stability aspects. To model the gestation lag of the predator species and the spatially heterogeneous characteristics of an ecological population, we incorporate the concept of diffusionally coupled delay into the system. The bifurcation behavior of the delayed homogeneous system is studied. The existence of traveling wave solutions for the delay–diffusion model is established. Numerical simulations are performed to justify analytical findings.

EFFECT OF VIRAL INFECTION ON THE GENERALIZED GAUSE MODEL OF PREDATOR-PREY SYSTEM

2003 ◽  
Vol 11 (01) ◽  
pp. 19-26 ◽  
Author(s):  
J. CHATTOPADHYAY ◽  
A. MUKHOPADHYAY ◽  
P. K. ROY
Keyword(s):  
Viral Infection ◽  
Specific Growth ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Stability Behavior ◽  
Force Of Infection ◽  
Prey System ◽  
Infected Prey

The generalized Gause model of predator-prey system is revisited with an introduction of viral infection on prey population. Stability behavior of such modified system is carried out to observe the change of dynamical behavior of the system. To substantiate the analytical results of this generalized susceptible prey, infected prey and predator population, numerical simulations of the model with specific growth and response functions are performed. Our observations suggest that the disease on prey population has a destabilizing or stabilizing effect depending on the level of force of infection and may act as a biological control for the persistence of the species.

Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudeshna Mondal ◽  
Guruprasad Samanta
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Prey ◽  
Terrestrial Vertebrates ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Refuge Area ◽  
Prey Interaction ◽  
Transcritical Bifurcations

AbstractA field experiment on terrestrial vertebrates observes that direct predation on predator–prey interaction can not only affect the population dynamics but the indirect effect of predator’s fear (felt by prey) through chemical and/or vocal cues may also reduce the reproduction of prey and change their life history. In this work, we have described a predator–prey model with Holling type II functional response incorporating prey refuge. Irrespective of being considering either a constant number of prey being refuged or a proportion of the prey population being refuged, a different growth rate and different carrying capacity for the prey population in the refuge area are considered. The total prey population is divided into two subclasses: (i) prey x in the refuge area and (ii) prey y in the predatory area. We have taken the migration of the prey population from refuge area to predatory area. Also, we have considered a benefit from the antipredation response of the prey population y in presence of cost of fear. Feasible equilibrium points of the proposed system are derived, and the dynamical behavior of the system around equilibria is investigated. Birth rate of prey in predatory region has been regarded as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the interior equilibrium point. Moreover, the conditions for occurrence of transcritical bifurcations have been determined. Further, we have incorporated discrete-type gestational delay on the system to make it more realistic. The dynamical behavior of the delayed system is analyzed. Finally, some numerical simulations are given to verify the analytical results.

scholarly journals Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag–Leffler Kernel

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Equilibrium Point ◽  
Power Law ◽  
Equilibrium Points ◽  
Essential Difference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Infected Prey

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals Singular perturbations of the unicritical polynomials with two parameters

2016 ◽  
Vol 37 (6) ◽  
pp. 1997-2016 ◽  
Author(s):  
YINGQING XIAO ◽  
FEI YANG
Keyword(s):  
Julia Set ◽  
Dynamical Behavior ◽  
Rational Maps ◽  
Topological Properties ◽  
Fatou Set ◽  
The Family ◽  
Image Position ◽  
Two Parameters ◽  
Unicritical Polynomials

In this paper, we study the dynamics of the family of rational maps with two parameters $$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$ where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

Sign in / Sign up

Export Citation Format

Share Document