Forman’s combinatorial vector fields on simplicial complexes are a discrete analogue of classical flows generated by dynamical systems. Over the last decade, many notions from dynamical systems theory have found analogues in this combinatorial setting, such as for example discrete gradient flows and Forman’s discrete Morse theory. So far, however, there is no formal tie between the two theories...

This paper explores the intermediate-time dynamics of newly formed solar systems with a focus on possible mechanisms for planetary migration. We consider two limiting corners of the available parameter space – crowded systems containing N = 10 giant planets in the outer solar system, and solar systems with N = 2 planets that are tidally interacting with a circumstellar disk. Crowded planetary s...

This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a “dynamical” sense. This means precisely that they (semi-) conjugate a given continuous (or measure-preserving) dynamical system and a symbolic one. The classes of dynamical systems and their codings c...

in this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.in the first approach, the equilibrium point of the system is one of the centers of the related membership fu...

This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a “dynamical” sense. This means precisely that they (semi-) conjugate a given continuous (or measure-preserving) dynamical system and a symbolic one. The classes of dynamical systems and their codings c...

Motivated by the work of Angeli and Sontag [1] and Enciso and Sontag [7] in control theory, we show that certain finite and infinite dimensional semi-dynamical systems with “negative feedback” can be decomposed into a monotone “open loop” system with “inputs” and a decreasing “output” function. The original system is reconstituted by “plugging the output into the input”. Employing a technique o...