Bifurcation memory

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",[A: 3] 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.

[A: 6] to describe the fact that solutions of a system of differential equations (when the boundary of the region in which they exist is crossed in the parameter space) retain similarity with the already nonexistent type of solutions as long as the variable parameter values insignificantly differ from the limit value.

[note 1]The earliest of those described on this subject in the scientific literature should be recognized, perhaps, the result presented in 1973,[A: 7] which was obtained under the guidance of L. S. Pontryagin, a Soviet academician, and which initiated then a number of foreign studies of the mathematical problem known as "stability loss delay for dynamical bifurcations".

[A: 1] A new wave of interest in the study of the strange behaviour of dynamic systems in a certain region of the state space has been caused by the desire to explain the non-linear effects revealed during the getting out of controllability of ships.

[A: 9][A: 10] The topicality of scientific studies of the bifurcation memory is obviously driven by the desire to prevent conditions of reduced controllability of the vehicle.