We propose a novel chaotic oscillator derived from the generic four-dimensional autonomous jerk systems. By using the Routh–Hurwitz criterion, we analyze the equilibrium point stability. Furthermore, we use the bifurcation diagram and Lyapunov exponents to explore the chaotic regions of the oscillator. One of the novel hyperjerk systems’ main features is the presence of antimonotonicity in a region of the parameter’s space. This phenomenon occurs when periodic orbits are generated and then annihilated via reverse period-doubling bifurcation scenarios as a control parameter is slowly scanned. Next, we propose an electronic design of the hyperjerk system which is compared with the numerical simulations, from which we observe a qualitative agreement among them. Latter, we analyze the synchronization behavior of the chaotic oscillator via feedback control. By using the Lyapunov function methodology, we establish the conditions to achieve synchronization based on the positivity of a matrix written in terms of the system parameters. The numerical simulations support our theoretical results.

我们提出了一种新颖的混沌振荡器，它是从通用的四维自治抽动系统中派生而来的。通过使用Routh–Hurwitz准则，我们分析了平衡点的稳定性。此外，我们使用分叉图和李雅普诺夫指数来探索振荡器的混沌区域。新型hyperjerk系统的主要特征之一是在参数空间的区域中存在反单调性。当生成周期性轨道，然后在缓慢扫描控制参数时，通过反向周期加倍的分叉方案消灭周期性轨道时，会发生此现象。接下来，我们提出了超高冲击系统的电子设计，并将其与数值模拟进行比较，从中我们观察到它们之间的定性一致。后期，我们通过反馈控制来分析混沌振荡器的同步行为。通过使用Lyapunov函数方法，我们根据系统参数编写的矩阵的正性，建立了实现同步的条件。数值模拟支持了我们的理论结果。