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Multistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua's oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov's exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics and synchronization of a fractional-order four dimensional nonlinear system based on a twostage Colpitts oscillator is investigated, using the Grünwald-Letnikov method. The study of the fractional-order stability of the equilibrium states of the system is carried out. The bifurcation diagram confirms the occurrence of Hopf bifurcation in the proposed system when the fractional-order passes a sequence of critical values, and reveals in addition various bifurcation scenarios including period-doubling and interior crisis transitions to chaos. In order to promote chaos-based fractional-order synchronization of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. Numerical simulations are performed to demonstrate the effectiveness and applicability of the proposed technique. [ABSTRACT FROM AUTHOR]

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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., Competing Interests: The authors declare no competing interests., (© 2023 The Authors.)

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 2 R 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., (© 2020 Published by Elsevier Ltd.)