There exist various methods for designing dynamical systems and dynamical games in order to ensure correctness and optimality.
Recently, fractional coupled systems of differential equations have gained more attention in different fields of science and engineering such as physics, control systems and dynamical systems.
Moreover, in the context of lossless analog compression, the information dimension is interpreted as the entropy rate of a dyadic expansion of the system [38], a relation that brings a intrinsic connection between information systems and dynamical systems.
It introduces the concepts of finite dynamical systems, polynomial systems, and dynamical systems over finite fields and applies them to creating a model of the lac operon.
Applying the method to E. coli central carbon metabolic system, we found that multiple enzymes including phosphoglycerate kinase, enolase, transketolase-b, etc., had critical roles in the system in terms of both system states and dynamical stability.
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance.
Despite languages and glassy systems stand apparently very far apart, it is very intriguing to explore the analogy between a linguistic system and a dynamical system featuring glassy properties.
Due to the unknown architecture of a system and the dynamical rules that capture the interactions between the components, it is difficult to control the complex system [ 16, 17].
In the last two decades, the theory of pullback attractors has been developed for non-autonomous dynamical systems and random dynamical systems (see, e.g. [10 12] and the references therein).
For more details of the concepts and properties of continuous dynamical systems and impulsive dynamical systems; see [52, 64, 101, 102, 106].
