A Novel Chua Circuit With Hyperbolic Tangent Nonlinearity for Brain-Inspired Dynamics and Stable Delta Rhythm Generation

초록

This work introduces a modified Chua circuit, distinguished by a hyperbolic tangent nonlinearity, designed to exhibit complex dynamics pertinent to neuromorphic engineering. The proposed system affords exceptional parametric control over attractor topology, enabling the systematic manipulation of multi-scroll chaotic structures via a single control parameter. Furthermore, the system exhibits bistability through the coexistence of distinct attractors under specific initial conditions. Through a comprehensive bifurcation analysis, we identify and characterize the critical Hopf bifurcation points that govern the transitions between stable, periodic, and chaotic regimes. A principal contribution of this research is the identification of a well-defined, bifurcation-free parameter corridor. Within this zone, the system generates robust, low-frequency oscillations analogous to neural delta rhythms while maintaining sustained chaotic behavior without secondary bifurcations, which ensures highly predictable frequency tuning. The theoretical framework is substantiated by a practical analog circuit implementation, demonstrating excellent fidelity between the mathematical model and its physical realization. A comparative performance analysis reveals that the proposed oscillator possesses superior characteristics including continuous stability windows, comprehensive delta-band coverage, and minimal parameter sensitivity when compared to classical and contemporary designs. These findings establish the proposed circuit as a robust and versatile platform for investigating nonlinear brain dynamics, developing tunable neuromorphic oscillators, and advancing chaos-based technologies.

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