Related papers: From discrete to continuous dynamics and back: How…
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…
We study the dynamics of a one-dimensional discrete flow with open boundaries - a series of moving point particles connected by ideal springs. These particles flow towards an inlet at constant velocity, pass into a region where they are…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
We investigate finite size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We study the dynamics of phase ordering of a non-conserved, scalar order parameter in one dimension, with long-range interactions characterized by a power law $r^{-d-\sigma}$. In contrast to higher dimensional systems, the point nature of…
Discrete dynamical systems defined on the state space {0,1,...,p-1}^n have been used in multiple applications, most recently for the modeling of gene and protein networks. In this paper we study to what extent well-known theorems by Smale…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…
We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…
We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We develop a class of C1-continuous time integration methods that are applicable to conservative problems in elastodynamics. These methods are based on Hamilton's law of varying action. From the action of the continuous system we derive a…
We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…