Related papers: Limit Cycle Bifurcations in a Quartic Ecological M…
In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a…
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…
By introducing a max-plus dynamical system having limit cycles, we discuss their periodicity, especially the number of discrete states in them. We also find that quasi-periodic cycles exist depending on the bifurcation parameter in the…
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…
In this paper, a quadratic system with two parallel straight line-isoclines is considered. This system corresponds to the system of class II in the classification of Ye Yanqian. Using the field rotation parameters of the constructed…
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.
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…
In this paper, we study the problem of limit cycle bifurcation in two piecewise polynomial systems of Li\'enard type with multiple parameters. Based on the developed Melnikov function theory, we obtain the maximum number of limit cycles of…
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;…
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…
The main purpose of this article is to study from the geometric point of view the problem of limit cycles bifurcation of perturbed completely integrable systems.
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic…
We prove that the number of limit cycles, which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or equal to three.
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, we generalize the Picard-Fuchs equation method to study the bifurcation of limit cycles of perturbed differential systems with two switching lines. We obtain the detailed expression of the corresponding first order Melnikov…
The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging…
This paper deals with the problem of limit cycle bifurcations for piecewise smooth integrable differential systems with four zones. When the unperturbed system has a family of periodic orbits, the first order Melnikov function is derived…
In this paper, we study a class of population models with time-varying factors, represented by one-dimensional piecewise smooth autonomous differential equations. We provide several derivative formulas in "discrete" form for the…
We study the bifurcation of limit cycles from the periodic orbits of $2n$--dimensional linear centers $\dot{x} = A_0 x$ when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control…
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles from focus boundary equilibria in other types of…