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Control of multistability in hidden attractors

Abstract

Hidden attractors have a basin of attraction which is not connected with unstable equilibrium. Certain systems with hidden attractor show multistability for a range of parameter. Multistability or coexistence of different attractors in nonlinear systems often creates inconvenience and therefore, needs to be avoided to obtain a desired specific output from the system. We discuss the control of multistability in the hidden attractor through the scheme of linear augmentation, that can drive the multistable system to a monostable state. With the proper choice of control parameters a shift from multistability to monostability can be achieved. This transition from multiple attractors to a single attractor is confirmed by calculating the basin size as a measure. When a nonlinear system with hidden attractors is coupled with a linear system, two important transitions are observed with the increase of coupling strength: transition from multistability to monostability and then stabilization of newly created equilibrium point via suppression of oscillations.

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Sharma, P.R., Shrimali, M.D., Prasad, A. et al. Control of multistability in hidden attractors. Eur. Phys. J. Spec. Top. 224, 1485–1491 (2015). https://doi.org/10.1140/epjst/e2015-02474-y

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  • DOI: https://doi.org/10.1140/epjst/e2015-02474-y