Nonlinear Dynamics and Hybrid Synchronization of DC Biased Colpitts Chaotic Oscillators

Chaos-based wireless communication systems offer promising opportunities for enhancing the physical-layer security of IoT devices. However, their successful integration depends on the ability to maintain robust chaotic behavior under environmental fluctuations, component tolerances, and parameter variations. This study investigates the nonlinear dynamics and hybrid synchronization of a modified Colpitts chaotic oscillator with a tunable base bias voltage. A comprehensive analysis is conducted through numerical simulations, SPICE-level modelling, and experimental validation using an analog prototype. While the simplified mathematical model shows only a DC offset shift with the added bias voltage, the SPICE simulations and hardware measurements reveal qualitative changes in the oscillator's dynamics. These findings underscore the importance of experimental verification, as idealized models often fail to capture critical behaviors in nonlinear systems. Hybrid synchronization is demonstrated between the analog oscillator and its FPGA-based digital counterpart, implemented using fixed-point arithmetic and the Euler–Cromer method. Despite model simplifications, effective synchronization is achieved via the Pecora–Carroll technique, highlighting that preserving the oscillator’s core dynamic structure is more critical than exact waveform replication. This result supports the practical use of chaos-based synchronization in resource-constrained secure communication systems.