An Effective Approach for Constructing a Class of 4D Multicluster Conservative Chaotic Systems without External Excitation

Abstract

Compared with dissipative chaos, conservative chaos is more suitable for information encryption since it does not have attractors, therefore, it is important to construct different complicated conservative chaotic systems. This paper reports an effective approach to construct a class of 4D conservative systems based on the formalism of a generalized Hamiltonian system. Based on the construction approach, several example systems including one hyperspatial multicluster chaotic system are proposed, and different cluster-shaped chaotic flows are discovered in these example systems. The only difference of these example systems is their Hamiltonians, whose local minimum points directly determine the number and position of these cluster-shaped conservative chaotic flows. Numerical simulations vividly demonstrate that different cluster-shaped chaotic flows really move around different local centers, i.e. the local minimum points of the Hamiltonian. In addition, an analog circuit is designed and simulated in NI Multisim to confirm the existence of multicluster conservative chaotic flows at the physical level.