Bifurcations without parameters in memristor-based oscillators

Abstract

Bifurcations without parameters are characterized by a continuous dependence of the system dynamics on initial conditions at fixed parameter values. Such bifurcations are typical for oscillators with manifolds of non-isolated limit sets such as lines or surfaces of equilibria, attractive manifolds of non-isolated closed curves, etc. The oscillatory regimes associated with bifurcations without parameters are extremely sensitive to inaccuracies, internal dynamic noise and external perturbations. As a result, the bifurcations without parameters are mostly studied on examples of idealized mathematical models, since it is difficult to experimentally realize such bifurcation transitions. Nevertheless, one can detect the manifestations of bifurcations without parameters in non-stationary oscillations and transients of real systems. For this reason, bifurcations without parameters and the presence of manifolds of non-isolated limit sets have transformed from mathematical exotic to the fundamental properties of dynamical systems and require comprehension. Nowadays, certain bifurcations without parameters are well-studied in the context of theory and experiments. In the current talk, we present a list of known bifurcations without parameters and discuss our contribution in this field.

Speaker

Vladimir V. Semenov
Saratov State University
Russia

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