Intermingled basins in coupled Lorenz systems

Camargo, Sabrina; Viana, Ricardo L.; Anteneodo, Celia

doi:10.1103/physreve.85.036207

Cited by 32 publications

(26 citation statements)

References 40 publications

(74 reference statements)

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“…The mechanism for induced multistability in the case of global coupling can be understood in a similar manner. However, in addition to synchronized attractors appearing due to the fixed points A ∓ , the systems can also exhibit other attractors, A 1,2 , similar to the ones discussed by Camargo et al [27] on which the dynamics is synchronized. A figure similar to Fig.…”

Section: Fig 4 Plots Similar Tomentioning

confidence: 52%

“…Although this is not easily demonstrated for the ensemble of coupled Lorenz oscillators due to the high dimensionality, a study of two coupled Lorenz oscillators gives some indication. For the case of r = 28, Camargo, Viana, and Anteneodo [27] showed that there were two attractors (inand out-of-phase) with intermingled basins of attraction that were riddled for sufficiently large coupling. A more detailed analysis of two coupled Lorenz attractors with r near the Hopf boundary [28] shows that there are several chaotic attractors with complicated basins.…”

Section: Introductionmentioning

confidence: 99%

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Emergence of chimeras through induced multistability

et al. 2017

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Chimeras, namely coexisting desynchronous and synchronized dynamics, are formed in an ensemble of identically coupled identical chaotic oscillators when the coupling induces multiple stable attractors, and further when the basins of the different attractors are intertwined in a complex manner. When there is coupling-induced multistability, an ensemble of identical chaotic oscillators-with global coupling, or also under the influence of common noise or an external drive (chaotic, periodic, or quasiperiodic)-inevitably exhibits chimeric behavior. Induced multistability in the system leads to the formation of distinct subpopulations, one or more of which support synchronized dynamics, while in others the motion is asynchronous or incoherent. We study the mechanism for the emergence of such chimeric states, and we discuss the generality of our results.

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Section: Fig 4 Plots Similar Tomentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Emergence of chimeras through induced multistability

et al. 2017

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“…It is also important to mention that Ω 1 ∩ Ω 2 = ∅, meaning that there is no initial condition that results in both attractors. Besides the complex structure and interaction between these basins of attraction, the property of intermingle and riddled basins that have been previously described in both discrete and continuous time systems as refereed in [27,28], cannot be attribute in this case due to their formal definition.The resulting size of each one of the attractors A 1,2 and the Lyapunov exponent remain invariant to the size of S p and Λ, respectively.…”

Section: Multistable Switching System With Symmetric Equilibriamentioning

confidence: 99%

Widening of the basins of attraction of a multistable switching dynamical system with the location of symmetric equilibria

Ontañón-García¹,

Campos-Cantón²

2017

Nonlinear Analysis: Hybrid Systems

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A switching dynamical system by means of piecewise linear systems in R 3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with stability index of type I, i.e., a negative real eigenvalue and a pair of complex conjugated eigenvalues with positive real part. This class of systems is constructed by a discrete control mode changing the equilibrium point regarding the location of their states. The scrolls are generated when the stable and unstable eigenspaces of each adjacent equilibrium point generate the stretching and folding mechanisms to generate chaos, i.e., the unstable manifold in the first subsystem carry the trajectory towards the stable manifold of the immediate adjacent subsystem.The resulting attractors are located around four focus saddle equilibria. If the equilibria are located symmetrically to one of the axes and the distance between each equilibria is properly adjusted to generate two double-scroll chaotic attractors, the system can present from bistable to multistable solutions re- *

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“…Camargo et al considered a system of two identical linearly coupled Lorenz oscillators presenting synchronization of chaotic motion for a specified range of the coupling strength. They verified the existence of global synchronization and antisynchronization attractors with intermingled basins of attraction, such that the basin of one attractor is riddled with holes belonging to the basin of the other attractor and vice versa [17]. Finally, Li et al concerned with model-free control of the Lorenz chaotic system, where only the online input and output are available, while the mathematic model of the system is unknown [18].…”

Section: Introductionmentioning

confidence: 99%