Dynamics and circuit implementation of three simplified chaotic systems

Abstract

To improve the performance of chaotic secure communication, three simplified chaotic systems with one variable parameter were investigated. Basic properties were analyzed including symmetry, dissipation and topological structure. Complex dynamical behaviors of the systems including chaos and periodic orbits were verified by numerical simulations, Lyapunov exponents and bifurcation diagrams. Interestingly, the three systems were integrated in a common circuit, and their dynamical behaviors were easily observed by adjusting regulable resistors R₂₈, R₁₄ and R₁₇, respectively, and the relations between the variable resistor and the system parameter were deduced. The circuit experiment results agree well with the simulation results. Finally, a secure communication scheme based on chaos shift keying (CSK) was presented, which lays an experiment foundation for chaotic digital secure communication.

Keywords

chaos / single-parameter system / circuit realization / secure communication / chaos shift keying

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