Extending the 3D Dong chaotic system to a 5D hyperchaotic system with three positive Lyapunov exponents: Dynamics, multistability, offset boosting, and PSO-DE based complexity optimization

In this paper, we propose a new five-dimensional system that is capable of producing multistability and hyperchaos with three positive Lyapunov exponents (LEs) for specific parameter settings. The proposed system was derived by making an extension of Dong's chaotic system with changes that increase its dimension, complexity, and applicability. Using numerical simulations, we confirmed that the model produces hyperchaos with three positive LEs depending on parameter values, which means that its dynamics expands in three directions of the phase space. Regions of periodicity, chaos, hyperchaos with two positive LEs, and hyperchaos with three positive LEs were identified by LE spectra and verified using phase diagrams. The ability of the system to generate coexisting attractors is also shown, where the system demonstrates various behaviors for various initial conditions at fixed parameters. Furthermore, offset boosting control is presented to show that the attractors can be shifted without altering the internal dynamics of the system. Moreover, a topological complexity optimization framework is proposed to maximize the Kaplan–Yorke dimension (KYD) using Particle Swarm Optimization (PSO) and Differential Evolution (DE), followed by the 0–1 test and Approximate Entropy calculation. With its multistability, properties, hyperchaos with three positive LEs, controllable offset boosting, and optimized complexity, the novel model has excellent potential for practical applications.