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We report a five-component autonomous chaotic oscillator of jerky type, hitherto the simplest of its kind, using only one operational amplifier. The key component of the circuit is a junction field-effect transistor operating in its triode region, which provides a nonlinear resistor of antisymmetrical current-voltage characteristic, emulating a Colpitts-like chaotic circuit. We describe the experimental results illustrating the dynamical behavior of the circuit. In addition, we report numerical simulations of a model of the circuit which display good agreement with our measurements.

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An array of excitable Josephson junctions under global mean-field interaction and a common periodic forcing shows emergence of two important classes of coherent dynamics, librational and rotational motion in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index to characterize the dynamical regimes and their transition and locate them in a parameter plane.PACS numbers: 05.45.Xt, 05.45.Gg A surprising new phenomenon was reported in the last decade, namely, the chimera states [1][2][3][4][5][6][7][8] that emerge via a symmetry breaking of a homogeneous synchronous state in a large population of nonlocally coupled identical phase oscillators into two coexisting spatially extended coherent and noncoherent subpopulations. Presently, existence of chimera states has been reported in identical limit cycle oscillators [8,9], chaotic systems [9-13] and very recently in excitable systems in presence of noise [14]. It drew special attention after noticing a similar behavior in the brain of some sleeping animals [15]. It has been now confirmed in laboratory experiments [16][17][18]. Most surprisingly, chimeralike states were observed in globally coupled network of identical oscillators [19][20][21][22][23] which was unexpected because of the presence of a perfect symmetry in such a network. The reason of symmetry breaking of a homogeneous state into coexisting coherent and nocoherent states still remains a puzzle.In We report a search, in this paper, for chimera states in a Josephson junction array under global mean-field interaction if they exist at all and under what conditions? The existence of a state of order and turbulence was reported earlier [30] in a forced Josephson junction array under global mean-field influence, which showed signatures of chimera states, however, no categorical statement was made at that time. We revisit that parameter space of the Josephson junction array under the same condition and confirm existence of chimeralike states. In the process, we notice two important classes of coherent states, one regular librational motion and a regular rotational motion in the array, which are typical dynamical features [32] of a single Josephson junction. In cylindrical space [37], the trajectory of a junction is localized during a libration while it encircles the cylinder during a rotational motion (Fig. 4). Most importantly, we observe a transition between the two coherent states for changing coupling interaction. Increasing the coupling strength from a weaker range, the coherent librational motion emerges above a threshold and continues for a range of coupling, then transits to coherent rotational motion for large coupling via successive chimeralike states and clusarXiv:1612.08557v1 [nlin.CD]

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A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a ''two-component'' circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

The heart rhythm is one of the most interesting aspects of the dynamic behavior of biological systems. Understanding heart rhythms is essential in the dynamic analysis of the heart. Each type of dynamic behaviour can describe normal or pathological physiology. The heart is made up of nodes ranging from SA node (natural pacemaker) to Purkinje fibers. The electric current originates in the sinus node and travels through the heart until it reaches the Purkinje fibers, causing after its passage through each of the nodes a heartbeat thus constituting the electrocardiogram (ECG). Since the origin of the electric current is the sinus node, in this article we study numerically and experimentally by microcontroller the influence of the sinus node on the propagation of electric current through the heart. A study of the sinus node in its autonomous state shows us that in their coupled state, the nodes of the heart qualitatively reproduce the time series of the action potential of this latter, which leads to the recording of the ECG. A study when the sinus node is subjected to periodic pulsed excitation E 1(t) = kP(t), assumed to come from blood pressure, with P(t) the blood pressure, shows that for some selected frequencies, it is found that the nodes of the heart and the ECG exhibit responses having the same shape and the same frequencies as those of the pulsatile blood pressure. This suggests the possibility of using such a conversion and excitation mechanism to replicate the functioning of cardiac conduction system. The chaotic analysis of the sinus node subjected to a sinusoidal type disturbance (E 0sin(ωt)) is also presented, it shows that in its chaotic state, the nodes of the heart, as well as the ECG, provide very high frequency signals. This requires the control of the sinus node (natural pacemaker) in such a situation

In this work, the dynamical behavior and real time control of a target trajectory of a modified Van der Pol model so the potential is proportional to the term ( ) x sin n is proposed. A generalization in the case of small oscillations on the ( ) x sin n function is studied. Due to ( ) x sin n function, the system presents periodical regions of stability and unstability, a very rich dynamical behavior. Analytical investigations based on the harmonic balance method came out some specific values of the excitation frequency for which the model is subjected to a phenomenon of frequency entrainment. Also, under effect of the sine function power, chaos appears for even small value of the nonlinearity coefficient, in contrast to the classical Van der Pol oscillator. An investigation as an artificial pacemaker is done based on the real frequency of the natural pacemaker. We found that the modified Van der Pol model, like the classic Van der Pol model, can play the role of an artificial pacemaker with some approximations. Due to the complexity of the analogical sine function, an experimental study was made by real implementation of an Arduino Card based on the Runge-Kutta 4th order algorithm. The results obtained show a good correlation with the numerical results. RECEIVED