Dynamical behavior analysis of the heart system by the bifurcation structures.

The functioning of the heart rhythm can exhibit a wide variety of dynamic behaviours under certain conditions. In the case of rhythm disorders or cardiac arrhythmias, the natural rhythm of the heart is usually involved in the sinoatrial node, the atrioventricular node, the atria of the carotid sinus, etc. The study of heart related disorders requires an important analysis of its rhythm because the regularity of cardiac activity is conditioned by a large number of factors. The cardiac system is made up of a combination of nodes ranging from the sinus node, the atrioventricular node to its Purkinje bundles, which interact with each other via communicative aspects. Due to the nature of their respective dynamics, the above are treated as self-oscillating elements and modelled by nonlinear oscillators. By modelling the cardiac conduction system as a model of three nonlinear oscillators coupled by delayed connections and subjected to external stimuli depicting the behavior of a pacemaker, its dynamic behavior is studied in this paper by nonlinear analysis tools. From an electrocardiogram (ECG) assessment, the heart rhythm reveals normal and pathological rhythms. Three forms of ventricular fibrillation, ventricular flutter, ventricular tachycardia and atrial fibrillation are observed. The results are confirmed by the respective maximum Lyapunov exponents. Considering the cardiac nodes as microchips, using microcontroller simulation technology, the cardiac conduction system was modelled as a network of four ATmega 328P microcontrollers. A similarity with the results obtained numerically can be observed.

A robust image encryption scheme based on compressed sensing and novel 7D oscillato with complex dynamics.

The present work studies a novel efficient compressed based cryptosystem which combines a dynamical parameter coming from high dimensional system, a dynamics S-box and a 2D compress sensing (2D-CS). Firstly, a secret key depending on input image is gotten via the SHA-256 function. That input image, decomposed into four sub-images uses chaotic sequences of the novel 7D multistable system to perform 2D compress sensing. Afterward, the previous compressed image is substituted by the key-dependent Mordell elliptic curve based dynamic S-box. At the end, the diffusion of the substituted image is proceed by chaotic sequences coming from the novel 7D multistable system. The compressed based cryptosystem presented here is considerably dependent on the original image. Moreover, the 7D chaotic system exhibits phenomenon of transient chaos. Equally, we have found plan equilibria hidden attractors which is a good chaos based property in cryptography. Let's recall that up to date, phenomenon of transient chaos and plan equilibria hidden attractors are rarely reported in Josephson junction systems. This denothing the novelty of this article. Through well-known metrics, the results found are evaluated and validated as well as their robustness over brute force attacks. The obtained results are termed as good in accordances with the existing ones over the literature.

Chimera dynamics in an array of coupled FitzHugh-Nagumo system with shift of close neighbors.

In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with R close neighbors. Each element (j) connects to another (m) and its 2R neighbors. Shifting these neighbors produces particular phenomena such as chimera and multi-chimera. Step traveling chimera is observed for a time dependent shift. Results show that, basing oneself on both shift parameter m and close neighbors R, a full control on the chimera dynamics of the network can be ensured.