Exoplanets known as hot Jupiters offer a unique testbed for the study of the magnetohydrodynamical thermoresistive instability. This instability arises when ohmic heating enhances the electrical conductivity in a positive feedback loop leading to a thermal runaway. The heat equation, coupled with the momentum and magnetic induction equations form a strongly coupled non-linear third order system, from which chaotic behavior emerges naturally. We first illustrate and discuss the dynamical impact of thermoresistive instability in a representative solution in which the instability recurs in the form of periodic bursts. We then focus on the physical parameter regime in which aperiodic behavior occurs and demonstrate its chaotic nature. The chaotic regime turns out to be restricted to a relatively narrow region of parameter space within the domain where the thermoresistive instability occurs, on either side of which different classes of non-chaotic periodic behavior are observed. Through a linear stability analysis, we showcase how chaos appears at the transition between these dynamically distinct oscillatory regimes, which may be understood as overdamped and damped nonlinear oscillations.
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Although we focus in this paper on the simple local model of Hardy et al.,29 a similar chaotic behavior also materializes in a spatially extended version where variations of temperature in longitude are expressed as a first order Fourier expansion.
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