We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips, frequency suppression, multiple periodic states and chaos. Such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle...

The current paper proposes a novel variational Bayes predictive coding RNN model, which can learn to generate fluctuated temporal patterns from exemplars. The model learns to maximize the lower bound of the weighted sum of the regularization and reconstruction error terms. We examined how this weighting can affect development of different types of information processing while learning fluctuate...

Complex spatio-temporal systems may exhibit irregular behaviors when driven far from equilibrium. Reaction-diffusion systems often lead to the formation of patterns and spatio-temporal chaos. When a limited number of observations is available, the reconstruction and identification of complex dynamical regimes become challenging problems. A method based on spatial recurrence properties is propos...

The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos generators. In the present work the phenomenon of secure communication with chaos masking has been investigated experimentally. In this investigation chaos which is...

A new neural network model is introduced in this paper. The aim of the proposed Sierpinski neural networks is to provide a simple and biologically plausible neural network architecture that produces emergent complex spatio-temporal patterns through the activity of the output neurons of the network. Such networks can play an important role in the analysis and understanding of complex dynamic act...

This paper studies the performance of selected chaos-based systems which share their frequency bands with conventional spread-spectrum systems. Such a scenario may occur in normal practice when chaos-based systems are introduced while the conventional systems are still in operation. The particular chaos-based systems under study are the coherent chaosshift-keying (CSK) system and the non-cohere...

Abstract We treat several classes of hyperbolic stochastic partial differential equations in the framework white noise analysis, combined with Wiener–Itô chaos expansions and Fourier integral operator methods. The input data, boundary conditions coefficients operators are assumed to be generalized processes that have both temporal spatial dependence. prove under consideration unique solutions a...

Much of early research on chaos from the viewpoint of physics was performed using spatially confined convective systems. In spatially extended convective systems, on the other hand, spatiotemporal chaos occurs. However, there is no unified definition for the term spatiotemporal chaos as for chaos. To unify definition, a property common to the three kinds of spatiotemporal chaos observed in elec...

The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful d...

In this paper, we examine the collaboration problems teachers encountered in the course of instructing students using collaborative computer software to connect distributed classrooms. We describe issues surrounding teacher collaborations arising from three types of sources: Organizational chaos of teaching, physical and temporal dispersion of events and causes, and individualism in teaching pr...