Related papers: Detecting chaos in a complex system
We present a measurement noise reduction scheme based on information flow of a chaotic system. This scheme operates on conditions of chaoticity and well-defined noise level, not depending on other detailed characteristics of noise. Starting…
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…
Chaos is a phenomenon that attracted much attention in the past ten years. In this paper, we analyze chaos-based signal processing, and proposed a chaos processor to take advantage of chaos phenomenon. We also analyzed and demonstrated two…
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…
In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret,…
A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these…
Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time…
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…
A nonlinear small-world network model has been presented to investigate the effect of nonlinear interaction and time delay on the dynamic properties of small-world networks. Both numerical simulations and analytical analysis for networks…
In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…
Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…
An approach based on the kernel methods for capturing the nonlinear interdependence between two signals is introduced. It is demonstrated that the proposed approach is useful for characterizing generalized synchronization with a successful…
In this paper we propose an application of adaptive synchronization of chaos to detect changes in the topology of a mobile robotic network. We assume that the network may evolve in time due to the relative motion of the mobile robots and…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
We have developed the {\it general method} for the description of {\it separatrix chaos}, basing on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of…
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on a certain unit transform, which can combine any two 1D chaotic maps to generate a new one with…
Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
Pulses of synchronization in chaotic coupled map lattices are discussed in the context of transmission of information. Synchronization and desynchronization propagate along the chain with different velocities which are calculated…