相关论文: Simulation and Visualization of Chaos in a Driven …

In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems…

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…

Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different…

Chaotic logic gates or `chaogates' are a promising mixed-signal approach to designing universal computers. However, chaotic systems are exponentially sensitive to small perturbations, and the effects of noise can cause chaotic computers to…

The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…

The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…

We propose a simple method to visualize spatio-temporal correlation between scales using wavelets, and apply it to two typical spatio-temporally chaotic systems, namely to coupled complex Ginzburg-Landau oscillators with diffusive…

The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…

It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighbourhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states,…

This paper explores the chaotic properties of an advection system expressed in difference equations form. In the beginning the Aref's blinking vortex system is examined. Then several new lines are explored related to the sink problem (one…

This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…

This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is…

Can a neural network trained by the time series of system A be used to predict the evolution of system B? This problem, knowing as transfer learning in a broad sense, is of great importance in machine learning and data mining, yet has not…

Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…

In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…