To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, exist...To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.展开更多
A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are invest...A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.展开更多
This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin-Berezovskaya predator-prey model in depth using analytical and numerical bifurcation analysis.The stability conditions of fix...This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin-Berezovskaya predator-prey model in depth using analytical and numerical bifurcation analysis.The stability conditions of fixed points,codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied.This model exhibits transcritical,fip,Neimark-Sacker,and 1:2,1:3,1:4 strong resonances.The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory.For each bifurcation,various types of critical states are calculated,such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point.To validate our analytical findings,the bifurcation curves of fixed points are determined by using MatcontM.展开更多
Since the last century, various predator-prey systems have garnered widespread attention. In particular, the predator-prey systems have sparked significant interest among applied mathematicians and ecologists. From th...Since the last century, various predator-prey systems have garnered widespread attention. In particular, the predator-prey systems have sparked significant interest among applied mathematicians and ecologists. From the perspectives of both mathematics and biology, a predator-prey system with the Allee effect and featuring the Bazykin functional response has been established. For this model, analyses have been conducted on its boundedness, the properties of its solutions, the existence of equilibrium points, as well as its local stability and Hopf bifurcations.展开更多
文摘To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.
文摘A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.
文摘This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin-Berezovskaya predator-prey model in depth using analytical and numerical bifurcation analysis.The stability conditions of fixed points,codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied.This model exhibits transcritical,fip,Neimark-Sacker,and 1:2,1:3,1:4 strong resonances.The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory.For each bifurcation,various types of critical states are calculated,such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point.To validate our analytical findings,the bifurcation curves of fixed points are determined by using MatcontM.
文摘Since the last century, various predator-prey systems have garnered widespread attention. In particular, the predator-prey systems have sparked significant interest among applied mathematicians and ecologists. From the perspectives of both mathematics and biology, a predator-prey system with the Allee effect and featuring the Bazykin functional response has been established. For this model, analyses have been conducted on its boundedness, the properties of its solutions, the existence of equilibrium points, as well as its local stability and Hopf bifurcations.
