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

ABSTRACT 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.