Bifurcation memory
Open-knowledge reference entry
Bifurcation memory is a generalized name for some specific features of the behaviour of the dynamical system near the bifurcation. An example is the recurrent neuron memory.
General information
The phenomenon is known also under the names of "stability loss delay for dynamical bifurcations" and "ghost attractor".
The essence of the effect of bifurcation memory lies in the appearance of a special type of transition process. An ordinary transition process is characterized by asymptotic approach of the dynamical system from the state defined by its initial conditions to the state corresponding to its stable stationary regime in the basin of attraction of which the system found itself. However, near the bifurcation boundary can be observed two types of transition processes: passing through the place of the vanished stationary regime, the dynamic system slows down its asymptotic motion temporarily, "as if recollecting the defunct orbit", with the number of revolutions of the phase trajectory in this area of bifurcation memory depending on proximity of the corresponding parameter of the system to its bifurcation value, — and only then the phase trajectory rushes to the state that corresponds to stable stationary regime of the system.
Bifurcation situations generate in state space bifurcation tracks that isolate regions of unusual transition processes (phase spots). The transition process in the phase spot is estimated qualitatively as a universal dependence of the index of loss of controllability on the control parameter.
In the literature, the effect of bifurcation memory is associated with a dangerous "bifurcation of merging".
The twice repeated bifurcation memory effects in dynamical systems were also described in literature; they were observed, when parameters of the dynamical system under consideration were chosen in the area of either crossing two different bifurcation boundaries, or their close neighbourhood.
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