Explore the vast range of titles available.

A simple four-dimensional chaotic system is proposed in this paper. Based on the analysis of Hamiltonian energy and conservative nature, the system is considered as Hamiltonian conservative system. The conservative and chaotic properties of the system are verified by phase diagram, Lyapunov exponents, bifurcation diagram and complexity diagram. Then, extreme multistability of the system is studied when selecting different initial values, and it can observe the nested coexistence of unequal and equal energy levels. The topology of these conservative motions is closely related to the isoenergy line of the Hamiltonian function. In addition, the offset-boosting under parameter control is studied by phase diagram, time-domain waveform and mean value. The simulation circuit and the experiment circuit verify the feasibility of the system. Finally, the system is applied to finite-time synchronization, which lays a foundation for the application in practical engineering.

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.

In this paper, we study the finite-time synchronization problem for linearly coupled complex networks with discontinuous nonidentical nodes. Firstly, new conditions for general discontinuous chaotic systems is proposed, which is easy to be verified. Secondly, a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions. Based on a finite-time stability theorem for equations with discontinuous right-hand and inequality techniques, several sufficient conditions are obtained to ensure the synchronization goal. Results of this paper are general, and they extend and improve existing results on both continuous and discontinuous complex networks. Finally, numerical example, in which a BA scale-free network with discontinuous Sprott and Chua circuits is finite-timely synchronized onto discontinuous Chen system, is given to show the effectiveness of our new results.

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.

To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function include multiple time delays, but the memristive connection weights also consider transmission delays. Stemming from the characteristics of neural networks, two different types of discontinuous controllers with state information and sign functions are devised to effectuate network synchronization objectives. Combining the finite-time convergence criterion and the theory of fractional-order calculus, Mittag-Leffler synchronization conditions for fractional-order multi-delayed memristive neural networks (FMMNNs) are derived, and the upper bound of the setting time can be confirmed. Unlike previous jobs, this article focuses on applying different inequality techniques in the synchronous analysis process, rather than comparison principles to manage the multi-delay effects. In addition, this study removes the restrictive requirement that the activation function has a zero value at the switching jumps, and the discontinuous control protocol in this paper makes the networks achieve synchronization over a finite time, with some advantages in terms of the convergence speed.

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results.

This paper aims to study the finite-time synchronization (FTS) of fractional-order delayed memristor-based Cohen–Grossberg neural networks (FODMCGNNs). Firstly, on the basis of the inequality on fractional-order derivative of the composite function, a novel fractional-order finite-time inequality is established; it extends the existing one and can be employed to discuss the FTS of fractional-order differential systems. More importantly, it is demonstrated theoretically that the estimated settling time by this inequality is more accurate than that with the existing one. Subsequently, on the basis of this novel inequality, the designed feedback controllers, and the fractional-order power law inequality, two novel criteria are obtained to ensure the FTS of FODMCGNNs. Finally, three examples are given to verify the correctness and advantage of the obtained results.

Nowadays, it is important to realize systems that can model the electrical activity of neurons taking into account almost all the properties of the intracellular and extracellular environment in which they are located. It is in this sense that we propose in this paper, the improved model of Hindmarsh–Rose (HR) which takes into account the fluctuation of the membrane potential created by the variation of the ion concentration in the cell. Considering the effect of the electric field that is produced on the dynamic behavior of neurons, the essential properties of the model such as equilibrium point and its stability, bifurcation diagrams, Lyapunov spectrum, frequency spectra, time series of the membrane potential and phase portraits are thoroughly investigated. We thus prove that Hopf bifurcation occurs in this system when the parameters are chosen appropriately. We also observe that by varying specific parameters of the electric field, the model presents a very rich and striking event, namely hysteresis phenomenon, which justifies the coexistence of multiple attractors. Besides, by applying a suitable sinusoidal excitation current, we prove that the neuron under electric field effect can present several important electrical activities including quiescent, spiking, bursting and even chaos. We propose the improved HR model under electric field effect (mHR) to study the finite-time synchronization between two neurons when performing synapse coupling across the membrane potential and the electric field coupling. As a result, we find that the synchronization between the two neurons is weakly influenced by the variation of the intensity of the electric field coupling while it is strongly impacted when the intensity of the synapse coupling is modified. From these results, it is obvious that the electric field can be another effective bridge connection to encourage the exchange and coding of the signal. Using the finite-time synchronization algorithm, we theoretically quantify the synchronization time between these neurons. Finally, Pspice simulations are presented to show the feasibility of the proposed model as well as that of the developed synchronization strategy.

This paper is devoted to studying the finite-time and fixed-time of inertial Cohen–Grossberg type neural networks (ICGNNs) with time varying delays. First, by constructing a proper variable substitution, the original (ICGNNs) can be rewritten as first-order differential system. Second, by utilizing feedback controllers and constructing suitable Lyapunov functionals, several new sufficient conditions guaranteeing the finite-time and the fixed-time synchronization of ICGNNs with time varying delays are obtained based on different finite-time synchronization analysis techniques. The obtained sufficient conditions are simple and easy to verify. Numerical simulations are given to illustrate the effectiveness of the theoretical results.

In this study, a model-free  PIφ-sliding mode control ( PIφ-SMC) methodology is proposed to synchronize a specific class of chaotic fractional-order memristive neural network systems (FOMNNSs) with delays and input saturation. The fractional-order Lyapunov stability theory is used to design a two-level  PIφ-SMC which can effectively manage the inherent chaotic behavior of delayed FOMNNSs and achieve finite-time synchronization. At the outset, an initial sliding surface is introduced. Subsequently, a robust  PIφ-sliding surface is designed as a second sliding surface, based on proportional–integral (PI) rules. The finite-time asymptotic stability of both surfaces is demonstrated. The final step involves the design of a dynamic-free control law that is robust against system uncertainties, input saturations, and delays. The independence of control rules from the functions of the system is accomplished through the application of the norm-boundedness property inherent in chaotic system states. The soft actor-critic (SAC) algorithm based deep Q-Learning is utilized to optimally adjust the coefficients embedded in the two-level  PIφ-SMC controller’s structure. By maximizing a reward signal, the optimal policy is found by the deep neural network of the SAC agent. This approach ensures that the sliding motion meets the reachability condition within a finite time. The validity of the proposed protocol is subsequently demonstrated through extensive simulation results and two numerical examples.