Numerical analysis of nonlinear dynamics and the transition to chaos in discharges of N2-GaAs systems

Electrical discharges in N2-GaAs systems exhibit complex nonlinear dynamics with key implications for the design of optoelectronic devices, particularly in contexts where avalanche and chaos affect performance. This work numerically explores a system of differential equations, derived from the continuity equation and Poisson’s equation, describing the time evolution of voltage and current density in an N2-GaAs system, considering simplifications such as spatial uniformity and varying carrier generation rates (α). Through numerical integration and the calculation of the highest Lyapunov exponent, we examine how the system transitions from stable states to chaotic behavior. The results show that low values of α, such as 0.5 s−1, produce damped oscillations, while increases up to 2.0 s−1 trigger chaotic dynamics, characterized by positive Lyapunov exponents and intricate trajectories in phase portraits and Poincaré maps. In addition, bifurcation diagrams of the system corroborate this transition to chaos. This transition depends on a critical threshold related to the nonlinear amplification and saturation effects present in the model. The findings deepen the understanding of discharges in N2-GaAs and highlight their relevance for optoelectronic applications, such as avalanche photodetectors and nonlinear oscillators, where mastering chaotic dynamics is essential. This analysis establishes a solid framework for future research, opening paths toward experimental studies and theoretical developments in semiconductor systems with similar properties.