We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized with desynchronized states and periodic with aperiodic motions. We show symmetric patterns for which both populations have the same type of dynamics as well as chimera states of a broken symmetry. The network can furthermore show multistability by settling to distinct dynamics for different realizations of random initial conditions or by switching intermittently between distinct dynamics for the same realization. We conclude that our system of two populations of a particularly simple map is the most simple system that can show this highly diverse and complex behavior, which includes but is not limited to chimera states. As an outlook to future studies, we explore the stability of two populations of quadratic maps with a complex-valued control parameter. We show that bounded and diverging dynamics are separated by fractal boundaries in the complex plane of this control parameter.

中文翻译：

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两个种群的二次映射图表现出大量对称和对称的断裂动力学

我们从数值上研究了两个相同实值二次图的两个相同总体的网络。在不同种群内部和不同种群之间的耦合强度发生变化时，网络呈现出多种多样的独特动态。各个种群中的地图可以同步或不同步。它们的时间演变可以是周期性的或非周期性的。此外，人们可以找到同步状态与非同步状态的混合以及周期性非周期运动的混合。我们显示了两个群体具有相同类型的动力学以及对称性破碎的嵌合状态的对称模式。对于随机初始条件的不同实现，网络还可以通过适应不同的动力学，或者对于同一实现，通过在不同的动力学之间进行间歇切换来显示网络的多重稳定性。我们得出的结论是，由两个人口组成的特别简单的地图系统是可以显示这种高度多样化和复杂行为的最简单系统，其中包括但不限于嵌合体状态。作为未来研究的展望，我们探索了具有复数值控制参数的两个二次映射种群的稳定性。我们表明，在此控制参数的复平面​​中，有界和发散动力学被分形边界分开。