Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey

Dhar, Joydip; Singh, Harkaran; Bhatti, Harbax Singh

doi:10.1016/j.amc.2014.12.021

Cited by 14 publications

(8 citation statements)

References 38 publications

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“…In the past few years, many studies have shown that discrete-time predator-prey systems have more abundant dynamic behaviors than continuous systems, such as bifurcation and chaos. They have obtained the relevant dynamic behaviors among populations through numerical simulation [17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate

Han

Lei

2022

Mathematics

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In this paper, we study the stability and bifurcation analysis of a class of discrete-time dynamical system with capture rate. The local stability of the system at equilibrium points are discussed. By using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Hopf bifurcation in the interior of R+2 are proved. The numerical simulations show that the capture rate not only affects the size of the equilibrium points, but also changes the bifurcation phenomenon. It was found that the discrete system not only has flip bifurcation and Hopf bifurcation, but also has chaotic orbital sets. The complexity of dynamic behavior is verified by numerical analysis of bifurcation, phase and maximum Lyapunov exponent diagram.

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Section: Introductionmentioning

confidence: 99%

“…Joydip-Dhar et al [18] studied the following discrete-time prey-predator model with crowding effect and predator partially dependent on prey:…”

Section: Introductionmentioning

confidence: 99%

Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate

Han

Lei

2022

Mathematics

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“…The interactions between prey and predator living in the same environment is a fascinating field in the bio-mathematical literature starting with the pioneer work of Lotka (1925) and Volterra (1926). Many mathematicians and ecologists studied the dynamical behavior of the preypredator system in ecology and contributed to the growth of the population models (Dhar and Jatav 2013;Dubey 2007;Freedman 1980;Jeschke et al 2002; Kooij and Zegeling 1996;Ma and Takeuchi 1998;Singh et al 2015;Dhar et al 2015;Sen et al 2012;Murray 2002;Robinson 1998;Tripathi et al 2015). Further, the correlation between the disease and the prey-predator system is a topic of significant interest, and the fusion of ecology and epidemiology is a comparatively new branch of study, known as eco-epidemiology.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a prey-generalized predator system with disease in prey and gestation delay for predator

Singh

Dhar

Bhatti³

2016

Model. Earth Syst. Environ.

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In the present study, a prey-generalized predator model is proposed with disease in the prey and gestation delay for predator. The asymptotic behavior of the model is studied for all the feasible equilibrium states. The criterion for local stability of the system are established around steady states and thresholds for Hopf bifurcation are determined at the endemic as well as disease-free state. The respective sensitive indices of the variables are identified at the endemic state by performing the sensitivity analysis. Further numerical simulations have been carried out to justify our analytic findings.

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“…In [14], the author has investigated the stability and bifurcation of discrete-time predator-prey system with crowding effect of predator where predator is partially dependent on prey, this can be described by the following system (3). By analyzing, the author got the following conclusion: the systems undergoes flip bifurcation and Hopf bifurcation at fixed points under specific conditions when varies in small neighborhood.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey

Yan

Chen

et al. 2016

Discrete Dynamics in Nature and Society

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The Allee effect is incorporated into a predator-prey model with linear functional response. Compared with the predator-prey which only takes the crowding effect and predator partially dependent on prey into consideration, it is found that the Allee effect of the prey species would increase the extinction risk of both the prey and predator. Moreover, by using a center manifold theorem and bifurcation theory, it is shown that the model with Allee effect undergoes the flip bifurcation and Hopf bifurcation in the interior ofR+2with different Allee effect values. In the two bifurcations, we can come to the conclusion that different Allee effect will have different bifurcation value and the increasing of the Allee effect will increase the value of bifurcation, respectively.

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Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey

Cited by 14 publications

References 38 publications

Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate

Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate

Dynamics of a prey-generalized predator system with disease in prey and gestation delay for predator

Dynamic Complexities in 2-Dimensional Discrete-Time Predator-Prey Systems with Allee Effect in the Prey

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