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Y Maistrenko

Publications and source records attributed to Y Maistrenko.

6 recordsLinked to original sources
PubMed2001

Loss of coherence in a system of globally coupled maps.

We study the formation of symmetric (i.e., equally sized) or nearly symmetric clusters in an ensemble of globally coupled, identical chaotic maps. It is shown that the loss of synchronization for the coherent state and the emergence of subgroups of oscillators with synchronized behavior are two distinct processes, and that the type of behavior that arises after the loss of total synchronization depends sensitively on the dynamics of the individual map. For our system of globally coupled logistic maps, symmetric two-cluster formation is found to proceed through a periodic state associated with the stabilization either of an asynchronous period-2 cycle or of an asynchronous period-4 cycle. With further reduction of the coupling strength, each of the principal clustering states undergoes additional bifurcations leading to cycles of higher periodicity or to quasiperiodic and chaotic dynamics. If desynchronization of the coherent chaotic state occurs before the formation of stable clusters becomes possible, high-dimensional chaotic motion is observed in the intermediate parameter interval.

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PubMed2001

Resolving clusters in chaotic ensembles of globally coupled identical oscillators.

Clustering in ensembles of globally coupled identical chaotic oscillators is reconsidered using a twofold approach. Stability of clusters towards "emanation" of the elements is described with the evaporation Lyapunov exponents. It appears that direct numerical simulations of ensembles often lead to spurious clusters that have positive evaporation exponents, due to a numerical trap. We propose a numerical method that surmounts the spurious clustering. We also demonstrate that clustering can be very sensitive to the number of elements in the ensemble.

Journal Article↗
PubMed2001

Transcritical riddling in a system of coupled maps.

The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.

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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↗
PubMedDate not supplied

Bifurcation structure of a model of bursting pancreatic cells.

One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic beta-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n+1)-spike bursting behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.

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