On the Synchronization Of Dynamical Systems With Hidden Attractors
DOI:
https://doi.org/10.66131/JDSC12202615-27Keywords:
Synchronization, Dynamical Systems, Hidden attractors, Applied MathematicsAbstract
Nonlinear systems may have different types of complex behaviors. As their trajectories move through state space they move towards and away from invariant sets, contracting towards these geometric objects are called attractors. Furthermore, if an attractor emerges due to the interaction between stable and unstable manifolds of an equilibrium point the attractor is called selfexcited. In recent years, attractor that are not related to the vicinity of equilibrium points have been identify and called hidden attractors. We investigate the synchronization problem of these types of systems in two different coupling configurations:
A drive-response scheme with an output feedback design of the coupling term in the response subsystem; and a bidirectional scheme where the states of both systems depend on their interaction. As observed before synchronized behavior on a hidden attractor is very difficult to achieve. In this sense our results show that for the drive-response configuration is relatively simple to impose a synchronized behavior on hidden attractors; however, on bidirectional configuration the hidden attractors basically disappears with the synchronized solution converging towards the selfexcited attractor. We illustrate our results with numerical simulations of many well-known systems with hidden and selfexcited attractors.
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