A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts (FOC) systems with mismatched uncer

Regions of stability phases discovered in a general class of Genesio−Tesi chaotic oscillators are proposed. In a relatively large region of two‐parameter space, the system has coexisting point attractors and limit cycles. The variation of two parameters is used to characterize the multistability by plotting the isospike diagrams for two nonsymmetric initial conditions. The parameters window in which the jerk system exhibits the unusual and striking feature of multiple attractors (e.g., coexistence of six disconnected periodic chaotic attractors and three‐point attraction) is investigated. The second aspect of this study presents the synchronization of systems that act as mediators between two dynamical units that, in turn, show function projective synchronization (FPS) with each other. These are the so‐called relay systems. In a wide range of operating parameters; this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The results show that the coupled systems can achieve function projective synchronization in a determined time despite the unpredictability of the scaling function. In the coupling path, the outer dynamical systems show finite‐time synchronization of their outputs, that is, displaying the same dynamics at exactly the same moment. Further, this effect is rather general and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.

This paper deals with a new approach to explore the precise dynamic response of the maglev system train and its control. Magnetic-suspension systems are characterized by high nonlinearity and open-loop instability which are the core components of maglev vehicles. Firstly, we use the electromagnetics and mechanics laws to derive the mathematical expressions of the proposed maglev system. Analytical investigation and theoretical calculation show that for the specific values of the control system parameters, the maglev system train can be significantly improved. It points out that the inherent nonlinearity, the inner coupling, misalignments between the sensors and actuators, and external disturbances are the main issues that should be considered for maglev engineering. Secondly, a control strategy based on the precise model of a nonsing ular robust sliding mode control is designed to reduce the upper bound of both the uncertainty and interference of the sliding mode controller. This approach presents an added value compared to the new sliding control methods in terms of overshoot and speed of convergence which is designed to control the vertical position of the proposed system. By using rigorous mathematical transformation associated with the adaptation laws in the frequency domain, a sufficient condition is drawn for the stability of the dynamical error based on the Lyapunov theory. This allows us a great possibility for interpreting the operation of the maglev train system. Numerical results are presented to show the effectiveness of our proposed control scheme.

In this paper, a nonlinear Josephson junction (JJ) based-Wien bridge circuit is analyzed and coupled in order to obtain synchronization through passive components. The electrical equations governing the operation of our circuit are obtained using the laws of electrical circuit analysis. Chaotic phenomenon is demonstrated in the proposed circuit using relevant indicators such as the phase portraits, bifurcation and the corresponding Lyapunov diagram. Several coupling topologies are considered to achieve the phase synchronization that provides a better understanding of the distribution of energy in the overall system. Additionally, the effect of the noise is considered which considerably brings an added value to the dynamic of the phase synchronization between oscillators. Full synchronization is observed when the resistor is connected in parallel with the inductor or capacitor while different results are obtained when the resistor is connected in series with the capacitor or inductor. Finally, fine-tuning and selection of coupling coefficients reflects a migration toward synchronization between two Josephson junction based-Wien circuits that imply the self-adaptation of the synapse when two types of synapses are active simultaneously.