Investigation of isolated and collective dynamics in a novel Rössler system with DSP implementation and PRNG application

Abstract

This work introduces a novel Rössler prototype-4 system incorporating a nonmonotonic function as nonlinear element. The dynamics of this new model are explored both as a single oscillator and within its collective dynamics. Theoretical analysis reveals that the proposed model possesses both stable and unstable equilibrium points. Using nonlinear analysis tools, we identify complex dynamics in the system, including coexisting period-doubling bifurcations leading to oscillations, the formation of a chaotic Rössler attractor, and double-scroll chaos. Furthermore, the coupled version of the model demonstrates the formation of multiple single-scroll and double-scroll attractors, evolving into complex multi-scroll chaotic structures. The intricate collective dynamics of this system are successfully applied to pseudo-random number generation, with the results passing the NIST statistical test suite. In addition, the system is experimentally implemented using a digital signal processor (DSP) microcontroller, which accurately reproduces the numerical simulations. The individual and collective dynamics of the proposed model represent a significant contribution to the field of nonlinear dynamical systems, with promising applications in data security systems.