Related papers: Bifurcations from an attracting heteroclinic cycle…

A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…

In this paper, we explore the three-dimensional chaotic set near a homoclinic cycle to a hyperbolic bifocus at which the vector field has negative divergence. If the invariant manifolds of the bifocus satisfy a non-degeneracy condition, a…

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…

We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…

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…

This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomous vector field whose flow exhibits a weakly attracting…

We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…

We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in…

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…

The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…

We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the…

We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold.…

In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour…

Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds of perturbations. This means that such attractors can exist…

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries…

We consider the dynamics of small perturbations of stable two-frequency quasiperiodic orbits on an attracting torus in the quasiperiodically forced Henon map. Such dynamics consists in an exponential decay of the radial component and in a…

We derive the bifurcation set for a not previously considered three-parametric Bogdanov-Takens unfolding, showing that it is possible express its vector field as two different perturbed cubic Hamiltonians. By using several first-order…

In this paper we present a mechanism for the emergence of strange attractors in a one-parameter family of differential equations acting on a 3-dimensional sphere. When the parameter is zero, its flow exhibits an attracting heteroclinic…

Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of…

We consider $C^2$ vector fields in the three dimensional sphere with an attracting heteroclinic cycle between two periodic hyperbolic solutions with real Floquet multipliers. The proper basin of this attracting set exhibits historic…