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Speaker |
Prof. Dr. Anatoly Neyshtadt,Space Research Institute of Russian Academy of Sciences, Russia and Department of Mathematical Sciences, Loughborough University, UK |
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Abstract |
Stability loss delay is an interesting, important and not yet completely investigated phenomenon. This phenomenon can be described as follows. In classical bifurcation theory the behaviour of systems, depending on parameter, is considered for values of the parameter close to some critical, bifurcational one. In theory of dynamical bifurcations the parameter is changing slowly in time and passes through a value, which would be bifurcational in the classical static theory. Let at the bifurcational value of the parameter an equilibrium or a limit cycle loses its asymptotic linear stability but remains nondegenerate. It turns out, that in analytic systems the stability loss is inevitably delayed: the phase points remain near the unstable equilibrium (cycle) for a long time after bifurcation; during this time the parameter changes by a quantity of order 1. Such delay is not in general found in non-analytic (even infinitely smooth) systems. In the talk a review on the theory of stability loss delay for dynamical bifurcations will be presented. |
