Multistability in chaotic coupled Lorenz systems near the Hopf bifurcation boundary: Emergence of new stable equilibria

Thierry Tanze Wontchui, Sangeeta Rani Ujjwal, Duplex S. Mbieda Petmegni, Nirmal Punetha, Michael Ekonde Sone, Joseph Yves Effa and Ram Ramaswamy

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: In the chaotic Lorenz system, a Hopf bifurcation occurs when the parameter ρH≃ 24.74, the other parameters being maintained at σ=10 and β= 8/3. We study the collective dynamics of two mutually coupled Lorenz systems with ρ just above ρH when all equilibria in each isolated system are unstable. The Lorenz systems are coupled through both x and z variables which have different symmetry properties, and this leads to induced multistability in the dynamics. In addition to the existing strange attractor, two fixed points are stabilized, and in addition there are two new chaotic attractors that are smaller (in size) than the familiar butterfly-shaped attractor. The coupled dynamics has some similarities to that of the uncoupled system below the Hopf bifurcation, although it displays richer patterns. For suitable coupling strength there can be as many as six distinct stable states. We describe the basins of attraction of these coexisting states and their boundaries using various measures and establish that the basins are intermingled.

Keywords: Lorenz systems; Hopf bifurcation; Synchronization; Multistability; Intermingled basins (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s096007792500520x

DOI: 10.1016/j.chaos.2025.116507

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