Related papers: Characterization of a periodically driven chaotic …
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Sample-to-sample fluctuations of the time-dependent conductance of a system with static disorder have been studied by means of diagrammatic theory and microwave pulsed transmission measurements. The fluctuations of time-dependent…
When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological…
Chimera states in coupled oscillator systems present both spatially coherent and incoherent domains. The number and size of these domains depend on many factors like the system parameters and initial conditions. Systematic investigations of…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities…
Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…