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Spatiotemporal chaos in a conservative Duffing-type system

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  • Reis, Eduardo V.M.
  • Savi, Marcelo A.

Abstract

This paper deals with an investigation of spatiotemporal chaos in a conservative Duffing-type system governed by a partial differential equation with cubic nonlinearity. Perturbation analysis establishes novel mathematical tools to evaluate different types of dynamical responses in spatiotemporal systems. These tools allow the definition of different Lyapunov exponents: local, convective and mean exponents; being able to provide a local characterization of each kind of response in space. Numerical simulations are carried out showing quasi-periodic and spatiotemporal chaotic responses. An energetic approach is also of concern providing another strategy that allows a proper understanding of system dynamics. In this regard, an energy space is defined from different kinds of energy. A parametric analysis is carried out showing that a higher coupling coefficient present a lower energy dispersion with respect to time.

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  • Reis, Eduardo V.M. & Savi, Marcelo A., 2022. "Spatiotemporal chaos in a conservative Duffing-type system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009559
    DOI: 10.1016/j.chaos.2022.112776
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    1. Reis, Eduardo V.M. & Savi, Marcelo A., 2024. "Spatiotemporal nonlinear dynamics and chaos in a mechanical Duffing-type system," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

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