Autonomous Bursting in a Homoclinic System

A continuous train of irregularly spaced spikes, peculiar of homoclinic chaos, transforms into clusters of regularly spaced spikes, with quiescent periods in between (bursting regime), by feeding back a low frequency portion of the dynamical output. Such autonomous bursting results to be extremely robust against noise; we provide experimental evidence of it in a CO2 laser with feedback. The phenomen here presented display qualitative analogies with bursting phenomena in neurons.Comment: Submitted to Phys. Rev. Lett., 14 pages, 5 figure

Collision, explosion and collapse of homoclinic classes

Homoclinic classes of generic $C^1$-diffeomorphisms are maximal transitive sets and pairwise disjoint. We here present a model explaining how two different homoclinic classes may intersect, failing to be disjoint. For that we construct a one-parameter family of diffeomorphisms $(g_s)_{s\in [-1,1]}$ with hyperbolic points $P$ and $Q$ having nontrivial homoclinic classes, such that, for $s>0$, the classes of $P$ and $Q$ are disjoint, for $s<0$, they are equal, and, for $s=0$, their intersection is a saddle-node.Comment: This is the final version, accepted in 200

What can we learn from homoclinic orbits in chaotic dynamics?

info:eu-repo/semantics/publishe

Dissipative systems

The basic features of dissipative dynamical systems and their impact on the understanding of our natural environment are reviewed. The analysis covers both deterministic and stochastic aspects. Special attention is devoted to the ability of these systems to undergo successive transitions to complex modes of behaviour. The possibility of a unified description of both conservative and dissipative processes is also assessed.SCOPUS: ar.jinfo:eu-repo/semantics/publishe