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Attractor memory in a nonautonomous multistable system

Author

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  • Pisarchik, A.N.
  • Jaimes-Reátegui, R.
  • Franco, J.J. Barba

Abstract

Attractors in a multistable system have memory due to inertial properties of the dynamical system. If the driving force in a nonautonomous system with coexisting periodic orbits is turned off for some time and then turned on again, the system either returns to the same attractor or goes to another coexisting attractor. The attractor memory is the maximum driving-off time after which the system comes back to the same attractor. The attractor memory depends on the phase of the driving force, i.e., on the time when the driving is turned off. The duration of relaxation oscillations when the system returns to the same attractor grows exponentially as the driving-off time is increased, saturating to the memory time. The length of the phase-space trajectory during the driving-off time (memory distance) correlates with the system variable, but not with the attractor memory. The attractor memory concept is illustrated on the example of a multistable erbium-doped fiber laser with four coexisting periodic orbits.

Suggested Citation

  • Pisarchik, A.N. & Jaimes-Reátegui, R. & Franco, J.J. Barba, 2022. "Attractor memory in a nonautonomous multistable system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922007706
    DOI: 10.1016/j.chaos.2022.112580
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    Cited by:

    1. Jin, Yanfei & Wang, Haotian & Xu, Pengfei, 2023. "Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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