OPEN PLENARY @ COMPENG2026 Prof. Jacques Kengne
On the Design of a High-Dimensional Hyperchaotic Hyperjerk System with Multiple Positive Lyapunov Exponents: A Case Study
The study of hyperchaotic systems with multiple Lyapunov exponents is among the most frequently addressed topics in nonlinear physics. In this work, we describe a simple approach for the design of a hyperjerk-type
hyperchaotic system with several positive Lyapunov exponents. As an illustration, we consider an eighthorder autonomous hyperjerk system with hyperbolic sinusoidal nonlinearity, which has the advantage of being
implemented using a simple pair of semiconductor diodes connected in reverse parallel. The argument of the hyperbolic sine function is a linear combination of judiciously chosen system state variables. A detailed study
is conducted, focusing on dissipation, equilibrium behavior, bifurcation diagrams with corresponding Lyapunov exponent graphs, and the coexistence of attractors. Complexes dynamics, such as the hyperchaos with four positive Lyapunov exponents, dependent on the choice of system parameters, are highlighted. An experimental study, using a suitable analog computer, is carried out to verify/validate the results of the theoretical analysis. This work not only presents a novel hyperjerk-type hyperchaotic system but also underscores the practical applicability of theoretical findings through experimental validation. The results pave the way for further
exploration of hyperchaotic systems and their potential applications in secure communications and complex dynamics.
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- Castel Ivano, Trentino-Alto Adige
- Italy