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In the 21st century, the worldwide concern about global warming has forced energy to transform in the direction of low-carbon and non-carbon. The utilization of renewable energy is developing rapidly, which makes the non-synchronous generator sources become the main part of the newly added power sources. Based on the fundamentals of AC power grid operation, this paper describes three technical challenges faced by the power system in transition: the inadequacy of the classic synchronization stability concept in representing the new synchronization connotation of AC power systems with large proportion of non-synchronous generator sources; the inapplicability of the electromechanical transient analysis method in analyzing the generalized synchronization stability; and the wideband resonance instability caused by negative resistance of power electronic equipment. The decisive factors for maintaining the generalized synchronization stability, the countermeasure to solve the inapplicability of the electromechanical transient analysis method and a systematic approach to tackle the broadband resonance instability are proposed in the paper.

In this paper, a new approach is proposed to investigate new type of hybrid chaos synchronization in discrete-time hyperchaotic dynamical systems. We present, based on stability theory of linear discrete-time systems and Lyapunov stability theory, a general control scheme to study the co-existence of inverse projective synchronization, inverse generalized synchronization and Q-S synchronization between arbitrary 3D hyperchaotic maps. Numerical examples and computer simulations are used to validate the theoretical results derived in this paper.

In this work, we are concerned with the finite-time synchronization (FTS) control issue of the drive and response delayed memristor-based inertial neural networks (MINNs). Firstly, a novel finite-time stability lemma is developed, which is different from the existing finite-time stability criteria and extends the previous results. Secondly, by constructing an appropriate Lyapunov function, designing effective delay-dependent feedback controllers and combining the finite-time control theory with a new non-reduced order method (NROD), several novel theoretical criteria to ensure the FTS for the studied MINNs are provided. In addition, the obtained theoretical results are established in a more general framework than the previous works and widen the application scope. Lastly, we illustrate the practicality and validity of the theoretical results via some numerical examples.

This work deals with a systematic approach for the investigation of compound difference anti-synchronization (CDAS) scheme among chaotic generalized Lotka-Volterra biological systems (GLVBSs). First, an active control strategy (ACS) of nonlinear type is described which is specifically based on Lyapunov's stability analysis (LSA) and master-slave framework. In addition, the biological control law having nonlinear expression is constructed for attaining asymptotic stability pattern for the error dynamics of the discussed GLVBSs. Also, simulation results through MATLAB environment are executed for illustrating the efficacy and correctness of considered CDAS approach. Remarkably, our attained analytical outcomes have been in outstanding conformity with the numerical outcomes. The investigated CDAS strategy has numerous significant applications to the fields of encryption and secure communication.

In this paper, the classical problem and the inverse problem of generalized synchronization for different dimensional chaotic dynamical systems in discrete time are investigated. The generalized synchronization results have been derived using active control method and Lyapunov stability theory. Numerical simulations are performed to verify the effectiveness of the proposed schemes.

The research of collective dynamics and cooperation mechanisms among coupled particles in various topological structures is highly significant across many fields. This study proposes a coupled system consisting of oscillators with frequency fluctuation under a framework of general network. We initially perform a theoretical analysis of system synchronization, from which we derive the first-order and second-order asymptotic stability conditions of the mean field. Under the first-order asymptotic stability condition, we derive the system stationary-state response and obtain the output amplitude amplification (OAA) to unveil the collective behaviors of coupled system. It is shown that there exist rich generalized stochastic resonance (GSR) phenomena. Through numerical simulations within scale-free complex networks, we validate the analytical results regarding collective behaviors. With the introduction of numerical definitions of synchronization probability and mean first synchronization time, we analyze the impact of different parameters on system synchronization. Our findings indicate that both synchronization probability and mean first synchronization time exhibit non-monotonous phenomena varying with network heterogeneity reflected in the power-law exponent. Moreover, it is also observed that the process of system synchronization can be induced by the synergism of noise and coupling in scale-free complex networks with different characteristics and scales.

The nonlinear circuit with serial–parallel memristors shows special internal characteristics and external performance, which indicates that the serial–parallel memristors can greatly change the dynamic characteristics of the nonlinear system. Mathematical model of the system is established to analyze the influence of the serial–parallel memristors on the dynamical behaviors with the change of system parameters, and then the basin of attraction is used to exhibit the coexisting multiple attractors with different initial conditions and the serial–parallel memristors, which can reveal that the serial–parallel flux-controlled or charge-controlled memristors have different effects on the generation of chaos and multistability phenomenon. Moreover, the hardware description of memristor-based system through FPGA is realized by Verilog language and the experimental results are observed from digital oscilloscope. Finally, based on the Lyapunov stability theory and adaptive control law, a nonlinear controller is designed to achieve the adaptive generalized synchronization between five memristor-based chaotic systems, and numerical results of the adaptive generalized synchronization are presented to prove the correctness and effectiveness of the proposed method.

In this paper, the complex simplified Lorenz system is proposed. It is the complex extension of the simplified Lorenz system. Dynamics of the proposed system is investigated by theoretical analysis as well as numerical simulation, including bifurcation diagram, Lyapunov exponent spectrum, phase portraits, Poincaré section, and basins of attraction. The results show that the complex simplified Lorenz system has non-trivial circular equilibria and displays abundant and complicated dynamical behaviors. Particularly, the coexistence of infinitely many attractors, i.e., extreme multistability, is discovered in the proposed system. Furthermore, the adaptive complex generalized function projective synchronization between two complex simplified Lorenz systems with unknown parameter is achieved. Based on Lyapunov stability theory, the corresponding adaptive controllers and parameter update law are designed. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed synchronization scheme. It provides a theoretical and experimental basis for the applications of the complex simplified Lorenz system.

In this paper, we propose a fractional form of a new three-dimensional generalized Hénon map and study the existence of chaos and its control. Using bifurcation diagrams, phase portraits and Lyapunov exponents, we show that the general behavior of the proposed fractional map depends on the fractional order. We also present two control schemes for the proposed map, one that adaptively stabilizes the fractional map, and another to achieve the synchronization of the proposed fractional map.

In this paper, the inverse generalized synchronization problem for different dimensional chaotic dynamical systems in continuous-time is proposed and investigated. New results are derived using new control method and stability theory. Numerical simulations are used to verify the effectiveness of the proposed schemes.