Related papers: "Isochronic" dynamical systems and nullification o…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit…
We propose a unified definition for synchronization. By example we show that the synchronization phenomena discussed in the dynamical systems literature can be described within the framework of this definition.
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction of a quantity that combines gain and phase information for each system in…
We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based…
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. Here, we analyse the spontaneous synchronisation dynamics of vibrations assisting energy transfer in a bio-inspired…
In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the…
Transition of the ground state of a classical $\Phi^4$ theory in 2+1 dimensions is studied from a metastable state into the stable equilibrium. The transition occurs in the broken $Z_2$ symmetry phase and is triggered by a vanishingly small…
We show that for two identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony is an unstable attractor and arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We…
We investigate the decay process from a time dependent potential well in the semiclassical regime. The classical dynamics is chaotic and the decay rate shows an irregular behavior as a function of the system parameters. By studying the…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…
Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this context we report on the fractal properties of the isochrons…
We study the evolution of mixed scalar as well as spinor fields within the context of the classical field theory. The initial condition problem is solved and the fields distributions, exactly accounting for the initial conditions, are…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…