In general, chaos generated from smooth and non-smooth nonlinear dynamical systems described by ordinary differential equations (ODEs) or partial differential equations (PDEs) can be divided into two categories: dissipative chaos (chaotic attractor) and conservative chaos (also known as Hamiltonian chaos). Dissipative chaos exists widely in nature and has been described by many physical and artificial systems. Compared with dissipative chaos, there are few studies on conservative chaos because it is not easily observed in the real world. Thus far, conservative chaos can be found in classic Hamiltonian systems and some theoretical models in the fields of astronomy, molecular dynamics, and hydrodynamics. The most typical conservative chaotic system is the Nosé-Hoover thermostated oscillator, which provides a way to simulate a system in the NVT ensemble.

Recently, increasing attention has been focused on these systems that are able to produce divergenceless phase-space flows, such as conservative chaos and invariant tori. Although there is a common phenomenon that invariant tori and conservative chaotic flows coexist in conservative systems, little attention has been paid to the analysis of their dynamic characteristics. Conservative chaos has the properties of pseudo-randomness and white-noise-like, therefore like dissipative chaotic signals, conservative chaotic signals are also suitable for information encryption. However, conservative chaos having no attractor means that it cannot be reconstructed by the delay embedding method based on the captured data. When conservative chaos is applied to practical applications in engineering, there are still various theoretical and technical issues on the advantage of conservative chaos over dissipative chaos.

This Special Issue aims to introduce and discuss novel results, control techniques, practical applications, and circuit implementations for a wide range of conservative chaotic systems. We welcome original research and review articles relating to the themes of this Special Issue.

Potential topics include but are not limited to the following:

• Chaos in classic Hamiltonian systems, Nosé-Hoover thermostated harmonic oscillators, and other conservative systems
• Ergodicity of conservative systems
• Field-programmable gate array (FPGA)-based implementation of conservative chaotic systems
• Synchronisation and control of conservative chaotic systems
• Conservative-chaos-based information security
• Conservative-chaos-based random number generators
• Conservative-chaos-based optimisation methods
• Fractional order conservative chaotic systems
• Conservative chaos in memristive systems
• Conservative chaos in social, physical, and nervous systems
• Chaos theory and chaotic systems