This paper reports a modified 2D periodically forced oscillator. Numerical simulation results using the phase portrait and Lyapunov exponents’ spectrum say that the proposed oscillator depicts megastability. Offset boosting in the new system is shown using the variable boostable phenomenon. Very limited research is available on such type of oscillator. Further, in this paper, a controller based on contraction theory is designed for the synchronisation between the two identical modified chaotic oscillators. The performances of the designed controller are compared with two widely used and well-known controllers for the chaotic systems. These controllers are (i) nonlinear active controller (NAC) and (ii) backstepping controller (BSC). It is found that the contraction theory-based controller performs better in terms of the less synchronisation time, negligible steady-state error and low control energy. Further, synchronisation between two identical Rossler chaotic systems is also presented to validate the effectiveness of the contraction theory. The simulation results validate the objectives of this paper.

中文翻译：

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一种改进的具有超稳态和可变升压的混沌振荡器及其基于收缩理论的控制同步，优于反推和非线性主动控制

本文报告了一种改进的 2D 周期性强制振荡器。使用相图和李雅普诺夫指数谱的数值模拟结果表明，所提出的振荡器描述了超稳定性。新系统中的偏移提升使用可变可提升现象显示。对此类振荡器的研究非常有限。此外，在本文中，基于收缩理论的控制器被设计用于两个相同的修正混沌振荡器之间的同步。将设计的控制器的性能与混沌系统的两种广泛使用和众所周知的控制器进行了比较。这些控制器是 (i) 非线性有源控制器 (NAC) 和 (ii) 反步控制器 (BSC)。发现基于收缩理论的控制器在较少的同步时间方面表现更好，可忽略的稳态误差和低控制能量。此外，还提出了两个相同的罗斯勒混沌系统之间的同步，以验证收缩理论的有效性。仿真结果验证了本文的目标。