Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

Abstract

We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.

Analysis and implementation of new fractional-order multi-scroll hidden attractors*

“…The basins of attraction of system (1) can be obtained by changing the parameter q and the initial conditions x(i) and y(i) in a range of (−5, 5) with the system parameters unchanged [40][41][42][43][44] as shown in Fig. 10.…”

Dynamics of coupled modified Rossler oscillators: the role of nonisochronicity parameter

“…In compliance with this, in a recent study 24 , the authors have reported the advent of chimera states due to the presence of nonisochronicity term in a diffusively coupled global network of Rössler oscillators. They also found that the presence of multistability [25][26][27][28][29][30][31][32] is the key mechanism for the appearance of coexisting states. Moreover, the emergence of chimera state in a star network of Rössler oscillators with nonisochronicity term is demonstrated with various coupling topologies 33 .…”

Collective Dynamics of coupled Lorenz oscillators near the Hopf Boundary: Intermittency and Chimera states

“…Since both synchronized and desynchronized motions are possible on these attractors, the system exhibits chimeric behavior. The basins of attraction in such systems were found to be interwoven and riddled [54] with multiplicity of coexisting attractors [58].…”