Related papers: Universal Regular Autonomous Asynchronous Systems:…
Let $(X,f_{1,\infty})$ be a nonautonomous dynamical system. In this paper we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new, very natural, definition of asymptotic periodicity.…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…
Adaptive control technique is adopted to synchronize two identical non-autonomous systems with unknown parameters in finite time. A virtual unknown parameter is introduced in order to avoid the unknown parameters from appearing in the…
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. The global dynamics of the network…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
The biologist Ren\'e Thomas conjectured, twenty years ago, that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition for this system to produce sustained oscillations. In this…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
A syntactic model is presented for the specification of finite-state synchronous digital logic systems with complex input/output interfaces, which control the flow of data between opaque computational elements, and for the composition of…
Entry in: Encyclopedia of Algorithms, Ming-Yang Kao, Ed., Springer, To appear. Synonyms: Wait-free registers, wait-free shared variables, asynchronous communication hardware. Problem Definition: Consider a system of asynchronous processes…
There are few known universality classes of absorbing phase transitions in one dimension and most models fall in the well-known directed percolation (DP) class. Synchronization is a transition to an absorbing state and this transition is…
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of…
The steady states of an isotone electric system are described by an isotone function with respect to the componentwise order. When there are steady states, we highlight a dominant steady state and we study its domain of attraction for the…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product…
Asynchronous programming is a ubiquitous systems programming idiom to manage concurrent interactions with the environment. In this style, instead of waiting for time-consuming operations to complete, the programmer makes a non-blocking call…