We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a ...

Large computational quantity and cumulative error are main shortcomings of addweighted one-rank local-region single-step method for multi-steps prediction of chaotic time series. A local-region multi-steps forecasting model based on phase-space reconstruction is presented for chaotic time series prediction, including add-weighted one-rank local-region multisteps forecasting model and RBF neural...

The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of...

Transparent models search for a balance between interpretability and accuracy. This paper is about the estimation of transparent models of chaotic systems from data, which are accurate and simple enough for their expression to be understandable by a human expert. The models we propose are discrete, built upon common blocks in control engineering (gain, delay, sum, etc.) and optimized both in th...

This paper deals with the problem of secure data transmission based on multi-input multi-output delayed chaotic systems. A new multi-input secure data transmission scheme is proposed. Moreover, in order to increase again the robustness of secure data transmission, some delays are introduced as a second firewall against known plain-text attack. With this method, the parameters used as secret key...

Wireless network-on-chip (WiNoC) is considered as a novel approach for designing future multi-core systems. In WiNoCs, wireless routers (WRs) utilize high-bandwidth wireless links to reduce the transmission delay between the long distance nodes. When the network traffic loads increase, a large number of packets will be sent into the wired and wireless links and can...

This paper presents a new method for encryption of color images based on a combination of chaotic systems, which makes the image encryption more efficient and robust. The proposed algorithm generated three series of data, ranged between 0 and 255, using a chaotic Chen system. Another Chen system was then started with different initial values, which were converted to three series of numbers from...

Since the pioneer work of Lorenz on predictability problems [1–2], many studies have examined the relationships between predictability and initial error in chaotic systems [3–7]; however, these previous studies focused on multi-scale complex systems such as the atmosphere and oceans [4–6]. Because large uncertainties exist regarding the dynamic equations and observational data related to such c...

A chaotic attractor may consist of some number of bands (disjoint connected subsets). In continuous maps multi-band chaotic attractors are cyclic, that means every generic trajectory visits the bands in the same order. We demonstrate that in discontinuous maps multi-band chaotic attractors may be acyclic. Additionally, a simple criterion is proposed which allows to distinguish easily between cy...