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.

本文着重于使用反并联二极管对作为混沌振荡所必需的非线性器件的大型混沌电子电路的建模和对称破坏分析。一种新的且相对简单的自治抽动回路被用作范例。与目前采用相同二极管（因而是一个完美的对称电路）的方法不同，我们考虑更现实的情况，尽管参数不可避免地散布，两个反并联二极管都呈现出不同的电性能。因此，由二极管对合成的非线性分量表现出不对称的电流-电压特性，从而导致整个电子电路的明显对称性断裂。新电路的数学模型由具有指数非线性项的连续时间3D自治系统组成。我们通过使用分叉图和相空间轨迹图作为主要指标，研究对称和非对称操作模式下模型参数和初始条件的混沌机制。我们报告了混乱时期，自发对称打破，合并危机以及两个，四个或六个相互对称吸引子在对称操作方式中并存的时期加倍的途径。在非对称系统中发现了更多有趣而复杂的非线性行为，例如共存的非对称分叉气泡（在这项工作中发现的一种新现象），磁滞动力学，临界现象以及多个（即两个，三个，四个或五个）共存。 ）不对称吸引子的参数的一些适当选择的值。进行实验室实验测试以支持理论分析。在这项工作中获得的结果清楚地表明，具有背靠背二极管的混沌电路可以表现出比相关文献中所报道的更为复杂的动力学，因此应按照本文所述的方法进行相应的重新考虑。