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The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…
For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which…
We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical…
Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the…
The MAP kinase cascade is an important signal transduction system in molecular biology for which a lot of mathematical modelling has been done. This paper surveys what has been proved mathematically about the qualitative properties of…
We study the complex nonlinear dynamics of the two-photon Dicke model in the semiclassical limit by considering cavity and qubit dissipation. In addition to the normal and super-radiant phases, another phase that contains abundant…
There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of…
In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary…
Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of…
Control by dissipation, or environment engineering, constitutes an important methodology within quantum coherent control which was proposed to improve the robustness and scalability of quantum control systems. The system-environment…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
The quantum master equation obtained by generalizing the geometric formulation of nonequilibrium thermodynamics to dissipative quantum systems is seriously nonlinear. We argue that nonlinearity occurs naturally in the step from reversible…
We consider a system of linear oscillators, or quantum states, described by Random Matrix Theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…