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Lyapunov spectrum of chaotic maps with a long-range coupling mediated by a diffusing substance

Abstract

We investigate analytically and numerically coupled lattices of chaotic maps where the interaction is non-local, i.e., each site is coupled to all the other sites but the interaction strength decreases exponentially with the lattice distance. This kind of coupling models an assembly of pointlike chaotic oscillators in which the coupling is mediated by a rapidly diffusing chemical substance. We consider a case of a lattice of Bernoulli maps, for which the Lyapunov spectrum can be analytically computed and also the completely synchronized state of chaotic Ulam maps, for which we derive analytically the Lyapunov spectrum.

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Acknowledgments

This work was made possible with the partial financial support of the following Brazilian government agencies: CNPq, CAPES, FAPESP (Grant 2016/16148-5), and Fundação Araucária (State of Paraná).

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Correspondence to R. L. Viana.

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Viana, R.L., Batista, A.M., Batista, C.A.S. et al. Lyapunov spectrum of chaotic maps with a long-range coupling mediated by a diffusing substance. Nonlinear Dyn 87, 1589–1601 (2017). https://doi.org/10.1007/s11071-016-3135-0

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Keywords

  • Lyapunov exponents
  • Coupled map lattices
  • Long-range coupling