Related papers: Limit Cycle Bifurcations in a Quartic Ecological M…
This paper is devoted to study the limit cycle problem of a cubic reversible system with an isochronous center, when it is perturbed inside a class of polynomials. An upper bound of the number of limit cycles is obtained using the Abelian…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
New criteria are established for upper bounds on the number of limit cycles of periodic Abel differential equations having two periodic invariant curves, one of them bounded. The criteria are applied to obtain upper bounds of either zero or…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
This article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as $x'= a_1 x-y-a_3x^2+(2 a_2+a_5)xy + a_6 y^2$, $y'= x+a_1 y + a_2x^2+(2…
In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus of discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
This paper investigates the multiplicity and the number of limit cycles for planar piecewise linear system divided into two regions by a straight line and each linear subsystem has a node. Through constructing Poincare half maps and a…
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…
We will consider two special families of polynomial perturbations of the linear center. For the resulting perturbed systems, which are generalized Li\'enard systems, we provide the exact upper bound for the number of limit cycles that…
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space…
We study the occurrence of limit cycles from a point on the discontinuity hyperplane $L$ between two smooth vector fields where the two vector fields both point towards one another. Generically, such a point (called switched equilibrium in…
In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit…
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the…
We study localisation transition in a class of quasi-periodic systems that has two competing periodic scales. We show that such class of systems show a re-entrant localisation transition where the energy scale of transition is set by the…
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.
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics…
We revisit the bifurcation theory of the Lotka-Volterra quadratic system \begin{eqnarray} X_0 :\left\{\begin{aligned} \dot{x}=& - y -x^2+y^2 ,\\ \dot{y}= &\;\;\;\;x - 2xy \end{aligned} \right. \end{eqnarray} with respect to arbitrary…
Piecewise linear differential systems separated by two parallel straight lines of the type of center-center-Hamiltonian saddle and the center-Hamiltonian saddle-Hamiltonian saddle can have at most one limit cycle and there are systems in…
This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a switching curve $y=x^{m}$, where $m>1$ is an arbitrary positive. By analysing the first order Melnikov function, we give an…