The behavior of orbits for iterated logistic maps has been widely studied since the dawn of discrete dynamics as a research field, in particular in the context of the complex family f : C → C, parametrized as f c (z) = z 2 + c, with c ∈ C. However, little is is known about orbit behavior if the map changes along with the iterations. We investigate in which ways the traditional theory of Fatou-Julia may still apply in this case, illustrating how the iteration pattern (symbolic template) can affect the topology of the Julia and Mandelbrot sets.We briefly discuss the potential of this extension towards a variety of applications in genetic and neural coding, since it investigates how an occasional or a reoccurring error in a replication or learning algorithm may affect the dynamic outcome.

Many natural systems are organized as networks, in which the nodes interact in a time-dependent fashion. The object of our study is to relate connectivity to the temporal behavior of a network in which the nodes are (real or complex) logistic maps, coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects. We investigate in particular the relationship between the system architecture and possible dynamics. In the current paper we focus on establishing the framework, terminology and pertinent questions for low-dimensional networks. A subsequent paper will further address the relationship between hardwiring and dynamics in high-dimensional networks.

No abstract

No abstract