Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the effect of time-varying attractive–repulsive interactions as well as the hybrid model of coexisting attractive–repulsive interactions in two coupled nonlinear oscillators. The dynamics of two coupled nonlinear oscillators, specifically limit cycles as well as chaotic oscillators, are studied in detail for various dynamical transitions for both cases. Here, we show that dynamic or static attractive–repulsive interactions can induce an important transition from the oscillatory to steady state in identical nonlinear oscillators due to competitive effects. The analytical condition for the stable steady state in dynamic interactions at the low switching time period and static coexisting interactions are calculated using linear stability analysis, which is found to be in good agreement with the numerical results. In the case of a high switching time period, oscillations are revived for higher interaction strength.

中文翻译：

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两个耦合非线性振荡器中的静态和动态吸引-排斥相互作用

许多系统都表现出有吸引力的和排斥的交互类型，可能是动态的也可能是静态的。在动态切换吸引或排斥相互作用的影响下，系统动态特性的详细理解具有实际意义。但是，也可以使用两个共存的竞争交互来有效地建模。在这项工作中，我们研究了时变的吸引-排斥相互作用的影响，以及两个耦合的非线性振荡器中共存的吸引-排斥相互作用的混合模型。针对这两种情况的各种动态过渡，详细研究了两个耦合的非线性振荡器（特别是极限循环）和混沌振荡器的动力学。这里，我们表明，由于竞争效应，在相同的非线性振荡器中，动态或静态的吸引－排斥相互作用可以引起从振荡状态到稳态的重要转变。利用线性稳定性分析计算了低开关时间周期内动态相互作用和静态共存相互作用的稳态稳态分析条件，发现与数值结果吻合良好。在高开关时间的情况下，振荡会恢复，以提高交互强度。发现与数值结果非常吻合。在高开关时间的情况下，振荡会恢复，以提高交互强度。发现与数值结果非常吻合。在高开关时间的情况下，振荡会恢复，以提高交互强度。