prey system
Recently Published Documents


TOTAL DOCUMENTS

1647
(FIVE YEARS 338)

H-INDEX

68
(FIVE YEARS 8)

2022 ◽  
Author(s):  
Shilpa Garai ◽  
N. C. Pati ◽  
G. C. Layek ◽  
Nikhil Pal

Abstract We report the existence of periodic structures in the transitional and chaotic regimes in bi-parameter spaces of a predator-prey system. A model is constructed taking into consideration of two important effects: namely, the prey refuge and fear of predation risk. The fixed points, their existence and stability behaviors are analyzed. The Neimark-Sacker bifurcation in the neighborhood of the interior fixed point is shown selecting refuge strength as a bifurcation parameter. The complex dynamical behaviors are explored in the biparameter space with the help of the largest Lyapunov exponent and isoperiodic diagrams. The period-bubbling transitional patterns, and triple heterogeneous attractors resulting in qualitative unpredictability are identified in the present system. The Wada basin sets for the triple coexisting attractors are found. The study reveals that the oscillations of the populations in certain control parameter regions are highly dependent upon the initial densities of the populations.


2022 ◽  
Vol 355 ◽  
pp. 03048
Author(s):  
Bochen Han ◽  
Shengming Yang ◽  
Guangping Zeng

In this paper, we consider a predator-prey system with two time delays, which describes a prey–predator model with parental care for predators. The local stability of the positive equilibrium is analysed. By choosing the two time delays as the bifurcation parameter, the existence of Hopf bifurcation is studied. Numerical simulations show the positive equilibrium loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold.


2022 ◽  
Author(s):  
A. George Maria Selvam ◽  
S. Britto Jacob ◽  
Mary Jacintha ◽  
D. Abraham Vianny

Author(s):  
Haixia Li ◽  
Wenbin Yang ◽  
Meihua Wei ◽  
Aili Wang

In this paper, we investigate a diffusive modified Leslie–Gower predator–prey system with double Allee effect on prey. The global existence, uniqueness and a priori bound of positive solutions are determined. The existence and local stability of constant steady–state solutions are analyzed. Next, we induce the nonexistence of nonconstant positive steady–state solutions, which indicates the effect of large diffusivity. Furthermore, we discuss the steady–state bifurcation and the existence of nonconstant positive steady–state solutions by the bifurcation theory. In addition, Hopf bifurcations of the spatially homogeneous and inhomogeneous periodic orbits are studied. Finally, we make some numerical simulations to validate and complement the theoretical analysis. Our results demonstrate that the dynamics of the system with double Allee effect and modified Leslie–Gower scheme are richer and more complex.


2021 ◽  
Author(s):  
Yehu Lv

Abstract In this paper, we consider a diffusive predator-prey system with spatial memory and predator-taxis. Since in this system, the memory delay appears in the diffusion term, and the diffusion term is nonlinear, the classical normal form of Hopf bifurcation in the reaction-diffusion system with delay can't be applied to this system. Thus, in this paper, we first derive an algorithm for calculating the normal form of Hopf bifurcation in this system. Then in order to illustrate the effectiveness of our newly developed algorithm, we consider the diffusive Holling-Tanner model with spatial memory and predator-taxis. The stability and Hopf bifurcation analysis of this model are investigated, and the direction and stability of Hopf bifurcation periodic solution are also researched by using our newly developed algorithm for calculating the normal form of Hopf bifurcation. At last, we carry out some numerical simulations, two stable spatially inhomogeneous periodic solutions corresponding to the mode-1 and mode-2 Hopf bifurcations are found, which verifies our theoretical analysis results.


Author(s):  
Jai Prakash Tripathi ◽  
Sarita Bugalia ◽  
Debaldev Jana ◽  
Nisha Gupta ◽  
Vandana Tiwari ◽  
...  

Sign in / Sign up

Export Citation Format

Share Document