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Pattern formation in symplectic coupled map lattices

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  • de Souza, Leonardo Costa
  • Sales, Matheus Rolim
  • Szezech, José Danilo
  • Viana, Ricardo Luiz
  • Caldas, Iberê Luiz
  • da Silva Baptista, Murilo

Abstract

We investigate the emergence of spatio-temporal patterns in a one-dimensional symplectic coupled map lattice (CML) composed of periodically kicked rotors with nonlocal interactions. The system retains the Hamiltonian structure, preserving the phase space volume. The system exhibits cluster states driven by the stickiness effect, where chaotic trajectories wanders around regular structures. By changing the coupling strength and interaction range, we demonstrate the formation of mosaic-like and zigzag patterns associated with transient or persistent clustering. These patterns are analysed using the Kuramoto order parameter, Lyapunov spectrum, and spatial correlation integrals. Our results reveal that pattern formation correlates with suppressed local chaos and small values of Lyapunov exponent, indicating weak chaotic dynamics. The correlation analysis confirms the presence of coherent structures at small scales, which disappear in the strongly chaotic regime. These findings demonstrate how stickiness can induce clustering, given rise to complex collective behaviour in Hamiltonian systems with nonlocal couplings.

Suggested Citation

  • de Souza, Leonardo Costa & Sales, Matheus Rolim & Szezech, José Danilo & Viana, Ricardo Luiz & Caldas, Iberê Luiz & da Silva Baptista, Murilo, 2025. "Pattern formation in symplectic coupled map lattices," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010707
    DOI: 10.1016/j.chaos.2025.117057
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    References listed on IDEAS

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    1. Harle, M. & Feudel, U., 2007. "Hierarchy of islands in conservative systems yields multimodal distributions of FTLEs," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 130-137.
    2. Vasconcelos, D.B. & Viana, R.L. & Lopes, S.R. & Batista, A.M. & Pinto, S.E. de S., 2004. "Spatial correlations and synchronization in coupled map lattices with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 201-218.
    3. Woellner, C.F. & Lopes, S.R. & Viana, R.L. & Caldas, I.L., 2009. "Clustering and diffusion in a symplectic map lattice with non-local coupling," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2201-2215.
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