A five-dimensional thermos-controlled system with a simple attractive torus and synchronous application

Abstract

As a classic volume-conservative system, the Nose–Hoover chain can generate conservative chaos and nested invariant tori. This article utilizes the Nose–Hoover chain to produce a new five-dimensional thermos-controlled system, discovering the coexistence of conservative flows and dissipative attractors. A local analysis of the system reveals a fold-Hopf bifurcation. The system model becomes meaningful only when $T>0$, resulting in continuous energy fluctuations within the system that manifest as chaotic or other complex behaviors. Then, the dynamical behaviors of the system are studied, and in addition to the coexistence phenomenon, the system also exhibits transient chaos. And its implementation is realized using FPGA (Field Programmable Gate Array) technology. Finally, adaptive finite-time projective synchronization is designed and implemented for homeogeneous systems, and heterogeneous adaptive finite-time projective synchronization is achieved with a five-dimensional conservative system.