This paper introduces a novel autonomous chaotic jerk circuit with an antiparallel diodes pair whose mathematical model involves an inverse hyperbolic sine function in the form: \(f\left( x \right) = k - 2x + 4\arcsin h\left( {mx} \right)\) where \(k\) (i.e. a constant excitation source) controls the symmetry of the model while \(m\) represents the slope of the inverse hyperbolic sine. The presence of the inverse hyperbolic sine is unusual provided that such types of circuits are connected to hyperbolic sine nonlinearity. The analysis of the model indicates that in case of a perfect symmetry (\(k = 0.0\)), the system undergoes spontaneous symmetry breaking, period doubling scenario to chaos, symmetry recovering crisis, coexistence of multiple pairs of symmetric attractors, and coexisting symmetric bubbles of bifurcation. More complex and incoherent nonlinear dynamic patterns occur in the presence of symmetry perturbation (\(k\ne 0.0\)) including for instance non-symmetric Hopf bifurcations, coexisting point attractor and limit cycle, coexisting asymmetric bubbles of bifurcations, critical transitions, and coexisting (i.e. up to five) non-symmetric periodic and chaotic attractors. The space magnetization resulting from the presence of various coexisting attractors is examined and illustrated by using basins of attraction. The predictions of theoretical investigations are supported by laboratory experimental tests based on a prototypal electronic circuit mounted on a breadboard.

本文介绍了一种具有反并联二极管对的新型自治混沌混叠电路，其数学模型涉及反双曲正弦函数，形式为：\（f \ left（x \ right）= k-2x + 4 \ arcsin h \ left（{ mx} \ right）\）其中\（k \）（即恒定激励源）控制模型的对称性，而\（m \）表示反双曲正弦的斜率。反双曲正弦的存在是不寻常的，只要此类电路与双曲正弦非线性相关即可。对模型的分析表明，在完美对称的情况下（\（k = 0.0 \）），系统经历了自发的对称破坏，周期加倍的混乱情况，对称恢复危机，多对对称吸引子的共存和对称分叉气泡的共存。在对称扰动（\（k \ ne 0.0 \）），例如包括非对称的Hopf分叉，共存的点吸引子和极限环，共存的不对称分叉气泡，临界跃迁和不对称的周期性和混沌吸引子（最多五个）共存。通过使用吸引盆，对由各种共存吸引子的存在引起的空间磁化进行了检查和说明。理论研究的预测得到了基于安装在面包板上的原型电子电路的实验室实验测试的支持。