Escaping from a chaotic saddle in the presence of noise

Abstract

Abstract:There are certain situations in noisy nonlinear dynamical systems, for which it is required a fast transition between a chaotic and a periodic state.Here, we present a novel procedure to achieve this goal in the context of the partial control method of chaotic systems. The partial control method is a recently developed control procedure, that allows to keep the dynamics of a system showing transient chaos, close to its chaotic saddle. In this kind of systems, and in absence of an external control, trajectories remain chaotic for a while in a certain region of phase space before eventually escaping towards an external attractor. The aim of the control algorithm proposed here, is to maintain the chaotic orbits as much time as we want close to the chaotic saddle before forcing an immediate escape. To do that, we use the safe sets defined in the partial control method in a completely different way. By only using this set, we show how possible is to handle the stabilisation and destabilisation of the chaotic dynamics of the partially controlled system.

Forcing the escape: Partial control of escaping orbits from a transient chaotic region

“…The partial control method, which is a feedback method, has been used in previous works [3][4][5][6][7][8][9], and is applied to a map defined in a certain region Q where there is transient chaos and in absence of any control the orbit will eventually escape from the region after a certain number of iterations. Furthermore, the map is subjected to a disturbance which is always larger than the applied control.…”