Abstract
The thermostatted system is a conservative system different from Hamiltonian systems, and has attracted much attention because of its rich and different nonlinear dynamics. We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system. It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian, such as isosurfaces and local centers, and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions, while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian. Moreover, the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes, which are the segments of equilibrium curves of the generalized thermostatted system. Furthermore, the interesting results are vividly demonstrated by the numerical simulations.
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