相关论文: Global bifurcations of limit cycles in a Holling-t…

In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit…

In this paper, we carry out a global qualitative analysis of a reduced planar quartic Topp system which models the dynamics of diabetes. In particular, studying global bifurcations, we prove that such a system can have at most two limit…

We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…

We consider the local bifurcation and global dynamics of a predator-prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, heteroclinic cycle at a threshold of…

In this paper, we complete the global qualitative analysis of the well-known FitzHugh-Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying the Wintner-Perko termination principle for multiple limit…

The main objective of this paper is to study the number of limit cycles in a family of polynomial systems. Using bifurcation methods, we obtain the maximal number of limit cycles in global bifurcation.

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment;…

We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincar\'e map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits…

In this paper, using our bifurcational geometric approach, we solve the problem on the maximum number and distribution of limit cycles in the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic…

We find an upper bound to the maximal number of limit cycles, which bifurcate from a hamiltonian two-saddle loop of an analytic vector field, under an analytic deformation.

A new model to investigate environmental effects of genetically distinguishable predators is presented. The Holling type II response function, modelling feeding satiation, leads to persistent system's oscillations, as in classical…

Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…

In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric…

This paper, as a complement to the works by Hsu et al [SIAM. J. Appl. Math. 55 (1995)] and Huang et al [J. Differential Equations 257 (2014)], aims to examine the Hopf bifurcation and global dynamics of a predator-prey model of Leslie type…

We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal…

In this paper we research global dynamics and bifurcations of planar piecewise smooth quadratic quasi--homogeneous but non-homogeneous polynomial differential systems. We present sufficient and necessary conditions for the existence of a…

We prove that every heteroclinic saddle loop (a two-saddle cycle) occurring in an analytic finite-parameter family of plane analytic vector fields, may generate no more than a finite number of limit cycles within the family.

The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. A deteriorating environment changes weak Allee effects into strong ones. In this paper, we study the interplay between the functional…

We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…

We study the dynamics of a delayed predator-prey system with Holling type II functional response, focusing on the interplay between time delay and carrying capacity. Using local and global Hopf bifurcation theory, we establish the existence…