Transients in an autostochastic oscillator with delayed feedback

Variation of the dependence of the transient process duration on the initial conditions in systems with discrete time

“…As noted above, the Eno map (2) transforms for b = 0 into the logistic map (1). Therefore, the Eno map with b = 0 and λ = 1-3 must exhibit, within the framework of a stable cycle of period 1, a change in the type of dependence of the transient process duration on the initial conditions T ε (x 0 , y 0 ), as is characteristic of the logistic map.…”

“…As a rule, the effort is concentrated on studying established regimes and on determining how one dynamical regime is changed by another in response to variations of the control parameters. At the same time, there are many phenomena related to the transient processes that frequently remain unstudied despite the fact that such processes can provide information about the whole system and about attractors realized in the phase space [1,2].…”

“…As a rule, the effort is concentrated on studying established regimes and on determining how one dynamical regime is changed by another in response to variations of the control parameters. At the same time, there are many phenomena related to the transient processes that frequently remain unstudied despite the fact that such processes can provide information about the whole system and about attractors realized in the phase space [1,2].Previously [3], we have studied transient processes in a one-dimensional (1D) system with discrete time, representing a logistic map (1)In particular, it was demonstrated that dependence of the transient process duration on the initial conditions T ε ( x 0 ) for this logistic map qualitatively changes when the control parameter λ varies and one dynamical regime is changed by another. It was also shown that dependence of the transient process duration on the initial conditions obeys certain scaling laws.…”

“…Previously [3], we have studied transient processes in a one-dimensional (1D) system with discrete time, representing a logistic map (1) In particular, it was demonstrated that dependence of the transient process duration on the initial conditions T ε ( x 0 ) for this logistic map qualitatively changes when the control parameter λ varies and one dynamical regime is changed by another. It was also shown that dependence of the transient process duration on the initial conditions obeys certain scaling laws.…”

“…other words, the control parameters were varied in such a manner that all observations referred to this dynamic regime, in which the behavior of system (2) corresponds to an immobile stable point ( x 0 , y 0 ), x 0 = y 0 = ( λ + b -1)/ λ , and the behavior of map (1), to an immobile stable point…”