A novel chaotic system with a two-variable modulus nonlinearity utilizing modified Chua's model, analysis, electronic design, and function-based combination-combination synchronization
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This paper presents a novel chaotic system based on a modified Chua's circuit model, incorporating a distinctive two-variable modulus function \( g(x, y) \) and exhibiting a 2-torus behavior. The system’s dynamical properties are analyzed using bifurcation diagram, Poincar\'e sections, Lyapunov exponents, and phase portraits. A comprehensive stability analysis is conducted by deriving and examining the generalized equilibrium points as functions of system parameters. Additionally, the renowned combination-combination concept, based on a two-drive-response configuration technique, is integrated, analyzed, and examined using sine, cosine, and exponential functions. The synchronization outcomes are then verified through Lyapunov stability. Numerical simulations are performed to compare theoretical and practical results. Finally, an electronic circuit is designed for the system, with experimental validation provided through oscilloscope measurements.
Abstract
This paper presents a novel chaotic system based on a modified Chua's circuit model, incorporating a distinctive two-variable modulus function \( g(x, y) \) and exhibiting a 2-torus behavior. The system’s dynamical properties are analyzed using bifurcation diagram, Poincar\'e sections, Lyapunov exponents, and phase portraits. A comprehensive stability analysis is conducted by deriving and examining the generalized equilibrium points as functions of system parameters. Additionally, the renowned combination-combination concept, based on a two-drive-response configuration technique, is integrated, analyzed, and examined using sine, cosine, and exponential functions. The synchronization outcomes are then verified through Lyapunov stability. Numerical simulations are performed to compare theoretical and practical results. Finally, an electronic circuit is designed for the system, with experimental validation provided through oscilloscope measurements.