On the analysis of semiconductor diode-based chaotic and hyperchaotic generators-a case study

This paper deals with the mathematical modeling and bifurcation analysis of a class of semiconductor diode-based chaotic and hyperchaotic generators. The simple 4D hyperchaotic electronic oscillator introduced by Tamasevicius et al. (referred to as the TNC oscillator hereafter) is considered as a prototype/paradigm. In contrast to current approaches based on piecewise-linear methods, we propose a smooth mathematical model (with exponential nonlinearity) to investigate the dynamics of the oscillator. Various methods for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, and phase portraits are exploited to establish the connection between the system parameters and various complicated dynamics (e.g., hyperchaos, coexistence of attractors, and transient chaos) of the TNC oscillator. The transitions to hyperchaos are contrasted with equivalent scenarios obtained from an experimental implementation of the circuit. Using bifurcation diagrams as arguments, the analysis reveals/suggests that the Shockley diode model is appropriate for these types of circuits as it provides a close-form (i.e., accurate) description of the system's dynamics and thus represents an interesting tool for design engineers.