This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number ...

In this paper, an encryption algorithm is proposed for real-time image encryption. The scheme employs a dual chaotic generator based on a three dimensional (3D) discrete Lorenz attractor. Encryption is achieved using non-autonomous modulation where the data is injected into the dynamics of the master chaotic generator. The second generator is used to permute the dynamics of the master generator...

In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desir...

In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for ...

In this article, we discuss the reconstruction of chaotic dynamics in a partial observation situation. As a function approximator, we employ a Normalized Gaussian network (NGnet), which is trained by an on-line EM algorithm. In order to deal with the partial observation, we propose a new embedding method based on smoothing lters, which is called integral embedding. The NGnet is trained to learn...

An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured timeseries. The algorithm has four special features: 1. The state of the system is extracted from the time-series using delays, followed by weighted Principal Component Analysis (PCA) data reduction. 2. The prediction model consists of both a linear model and a Multi-Layer-Perceptron (MLP...

A new BAM model is presented that uses a chaotic output function operating in chaotic mode during recall. Our results show that the model develops well-defined attractor basins, with the result that our chaotic BAM is more tolerant to noise than a regular fixed point BAM. This is concluded from simulations that showed the superior performance of the new model when compared to the original BAM a...