Shilnikov-type dynamics in three-dimensional piecewise smooth maps

Indrava Roy, Mahashweta Patra and Soumitro Banerjee

Chaos, Solitons & Fractals, 2020, vol. 133, issue C

Abstract: We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows a ‘two-sided’ Shilnikov dynamics, i.e. simultaneous looping and homoclinic intersection of the one-dimensional eigenmanifolds of fixed points on both sides of the border. We also present two complementary methods to analyse the return time of an orbit to the border: one based on recursion and another based on complex interpolation.

Keywords: Three dimensional piecewise smooth map; Shilnikov chaos; Stable manifold and unstable manifold (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300540

DOI: 10.1016/j.chaos.2020.109655

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