Multistability, period-adding, and spirals in a snap system with exponential nonlinearity

Bruna B. T. Francisco () and Paulo C. Rech ()
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Bruna B. T. Francisco: Universidade do Estado de Santa Catarina
Paulo C. Rech: Universidade do Estado de Santa Catarina

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 5, 1-7

Abstract: Abstract In this paper we investigate analytically and numerically a snap system which has a single nonlinearity of exponential type. The system under investigation is modeled by a three parameter fourth-order autonomous nonlinear ordinary differential equation. By keeping one of these three parameters fixed, we investigate numerically the organization of chaos and periodicity in three parameter planes that consider, each of them, the simultaneous variation of the other two parameters. We show that these parameter planes display self-organized periodic structures embedded in a chaotic region. We also show that these parameter planes present regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. Furthermore, an analytical investigation regarding the divergence of the flow and the stability analysis of the related equilibrium points was also carried out. Graphic abstract

Date: 2023
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DOI: 10.1140/epjb/s10051-023-00536-9

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