Biomedical subjects

T Kapitaniak

Publications and source records attributed to T Kapitaniak.

9 recordsLinked to original sources

PubMed2001

Symmetry-increasing bifurcation as a predictor of a chaos-hyperchaos transition in coupled systems.

In weakly coupled systems, it is possible to observe the coexistence of the chaotic attractors which are located out of the invariant manifold and are not symmetrical in relation to this manifold. When the control parameter is changed, these attractors can undergo a chaos-hyperchaos transition. We give numerical evidence that before this transition the coexisting attractors merge together creating an attractor symmetrical with respect to the invariant manifold. We argue that the attractors that are not located at the invariant manifold can exhibit dynamical behavior similar to bubbling and on-off intermittency previously observed for the attractors located at the invariant manifold, and we describe the mechanism of these phenomena.

Journal Article↗

PubMed2000

Chaos-hyperchaos transition

The chaos-hyperchaos transition occurs when the second Lyapunov exponent becomes positive. We argue that this transition is mediated by changes in the stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor. Bifurcations of unstable periodic orbits occur in the neighborhood of the chaos-hyperchaos transition point where we observe unstable variable dimensionality. We give evidence that the chaos-hyperchaos transition is initiated by (i) the saddle-repeller bifurcation of a particular unstable periodic orbit usually of low period, (ii) the appearance of a repelling node in the saddle-node bifurcation, after which the chaotic attractor becomes riddled, or (iii) the absorption of the repeller (unstable node or focus) originally located out of the attractor by the growing attractor.

Journal Article↗

PubMed1996