A broken symmetry approach for the modeling and analysis of antiparallel diodes-based chaotic circuits: a case study

This paper focuses on the modeling and symmetry breaking analysis of the large class of chaotic electronic circuits utilizing an antiparallel diodes pair as nonlinear device necessary for chaotic oscillations. A new and relatively simple autonomous jerk circuit is used as a paradigm. Unlike current approaches assuming identical diodes (and thus a perfect symmetric circuit), we consider the more realistic situation where both antiparallel diodes present different electrical properties in spite of unavoidable scattering of parameters. Hence, the nonlinear component synthesized by the diodes pair exhibits an asymmetric current-voltage characteristic which engenders the explicit symmetry break of the whole electronic circuit. The mathematical model of the new circuit consists of a continuous time 3D autonomous system with exponential nonlinear terms. We investigate the chaos mechanism with respect to model parameters and initial conditions as well, both in the symmetric and asymmetric modes of operation by using bifurcation diagrams and phase space trajectories plots as main indicators. We report period doubling route to chaos, spontaneous symmetry breaking, merging crisis and the coexistence of two, four, or six mutually symmetric attractors in the symmetric regime of operation. More intriguing and complex nonlinear behaviors are revealed in the asymmetric system such as coexisting asymmetric bubbles of bifurcation (a new kind of phenomenon discovered in this work), hysteretic dynamics, critical phenomena, and coexisting multiple (i.e. two, three, four, or five) asymmetric attractors for some appropriately selected values of parameters. Laboratory experimental tests are conducted to support the theoretical analysis. The results obtained in this work clearly indicate that chaotic circuits with back to back diodes can demonstrate much more complex dynamics than what is reported in the relevant literature and thus should be reconsidered accordingly following the method described in this paper.