Intermittent-like synchronization and desynchronization phenomena in a Colpitts network model.

This study investigates the dynamics of a modified Colpitts oscillator, exhibiting complex periodic and chaotic behaviors. Our research explores the dynamics and synchronization of coupled chaotic Colpitts oscillators, crucial for understanding their potential applications and behaviors. The main discovery is the emergence of a phase in which the systems achieve either complete synchronization or desynchronization. This behavior depends on the values of the coupling parameter. The subsequent challenge involves understanding how the coupling parameter influences the emergence of this synchronization phenomenon.

Phase transitions on a multiplex of swarmalators.

Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range r_{c} which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync π has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength σ_{r} is very small for a fixed r_{c} and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of r_{c}. For σ_{r}=0 and for sufficiently small values of r_{c}, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling σ_{a} and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as σ_{a} increases. These results are supported by simulations and animations added as supplemental materials.

Synchronization in a multilevel network using the Hamilton-Jacobi-Bellman (HJB) technique.

This paper presents the optimal control and synchronization problem of a multilevel network of Rössler chaotic oscillators. Using the Hamilton-Jacobi-Bellman technique, the optimal control law with a three-state variable feedback is designed such that the trajectories of all the Rössler oscillators in the network are optimally synchronized at each level. Furthermore, we provide numerical simulations to demonstrate the effectiveness of the proposed approach for the cases of one and three networks. A perfect correlation between the MATLAB and PSpice results was obtained, thus allowing the experimental validation of our designed controller and shows the effectiveness of the theoretical results.

Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients.

This paper, is an analysis of the dynamics of new models of nonlinear systems in which the state damping variables with elastic coefficients, given by functions c cos ⁡ ( p x ) , c sin ⁡ ( p x ) , c cos ⁡ ( p x ˙ ) and c sin ⁡ ( p x ˙ ) are investigated in their autonomous and excited states. They exhibit periodic regions of stability and instability in their autonomous states and a rich dynamic behavior. The analysis of limit cycles shows the presence of isolated curves around the origin (0.0), which explains the presence of periodic solutions (limit cycles). The dynamics obtained allows to describe qualitatively the cardiac activity (artificial pacemaker). A chaos analysis shows the appearance of regular and chaotic behaviors. These studies allowed us to show the effect of the damping of the state variable and the elastic coefficients on the dynamics of these models. The presence of analog functions makes the experimental study complex. An implementation based on microcontroller simulation technology has been proposed. The microcontroller results are consistent with the numerical results.

Chimera states in a neuronal network under the action of an electric field.

The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state, and a multicluster traveling chimera.

Dynamics of multilayer networks with amplification.

We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster, and chimera states. Here, we consider a network with two layers of Rössler chaotic oscillators as well as applications to multilayer networks of the chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, inter-layer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in-depth study on the case of a network of Rössler oscillators using a master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster, and phase synchronization with amplification. For the case of Rössler oscillators, we note that there are also certain values of coupling parameters and amplification where the synchronization does not exist or the synchronization can exist but without amplification. Using other systems with different topologies, we obtain some interesting results such as chimera state with amplification, cluster state with amplification, and complete synchronization with amplification.

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.

Extreme multistability in a Josephson-junction-based circuit.

We design and report an electrical circuit using a Josephson junction under periodic forcing that reveals extreme multistability. Its overall state equations surprisingly recall those of a well-known model of Josephson junction initially introduced in our circuit. The final circuit is characterized by the presence of two new and different current sources in parallel with the nonlinear internal current source sin[ϕ(t)] of the Josephson junction single electronic component. Furthermore, the model presents an interesting extreme multistability which is justified by a very large number of different attractors (chaotic or not) when slightly changing the initial conditions.

Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array.

An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the 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 transitions and locate them in a parameter plane.

Coherent motion of chaotic attractors.

We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically.

Finite-time synchronization of tunnel-diode-based chaotic oscillators.

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.