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 ...
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 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 which 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.
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