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Periodic and Chaotic Dynamics of the Ehrhard–Müller System

Junho Park

School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea

E-mail Address: junho.park@snu.ac.kr

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Hyunho Lee

School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea

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, and

Jong-Jin Baik

School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea

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https://doi.org/10.1142/S0218127416300159Cited by:6 (Source: Crossref)

Abstract

This paper investigates nonlinear ordinary differential equations of the Ehrhard–Müller system which describes natural convection in a single-phase loop in the presence of nonsymmetric heating. Stability and dynamics of periodic and chaotic behaviors of the equations are investigated and the periodicity diagram is obtained in wide ranges of parameters. Regimes of both periodic and chaotic solutions are observed with complex behaviors such that the periodic regimes enclose the chaotic regime while they are also immersed inside the chaotic regime with various shapes. An asymptotic analysis is performed for sufficiently large parameters to understand the enclosure by the periodic regimes and asymptotic limit cycles are obtained to compare with limit cycles obtained from numerical results.

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