This paper concentrates on the global predefined-time synchronization of delayed memristive neural networks with external unknown disturbance via an observer-based active control. First, a global predefined-time stability theorem based on a non-negative piecewise Lyapunov function is proposed, which can obtain more accurate upper bound of the settling time estimation. Subsequently, considering the delayed memristive neural networks with disturbance, a disturbance-observer is designed to approximate the external unknown disturbance in the response system with a Hurwitz theorem and then to eliminate the influence of the unknown disturbance. With the help of global predefined-time stability theorem, the predefined-time synchronization is achieved between two delayed memristive neural networks via an active control Lyapunov function design. Finally, two numerical simulations are performed, and the results are given to show the correctness and feasibility of the predefined-time stability theorem.In this paper, we consider blinking systems, i.e., non-autonomous systems generated by randomly switching between several autonomous continuous time subsystems in each sequential fixed period of time. We study cases where a non-stationary attractor of a blinking system with fast switching unexpectedly differs from the attractors of composing subsystems. Such a non-stationary attractor is associated with an attractor of the averaged system being a ghost attractor of the blinking system [Belykh et al., Phys. D Nonlinear Phenom. 195, 188 (2004); Hasler et al., SIAM J. Appl. Dyn. Syst. 12, 1031 (2013); Belykh et al., Eur. Phys. J. Spec. Top. 222, 2497 (2013)]. Validating the theory of stochastically blinking systems [Hasler et al., SIAM J. Appl. Dyn. Syst. 12, 1031 (2013); Hasler et al., SIAM J. Appl. Dyn. Syst. 12, 1007 (2013)], we demonstrate that fast switching between two Lorenz systems yields a ghost chaotic attractor, even though the dynamics of both systems are trivial and defined by stable equilibria. We also study a blinking Hindmarsh-Rose system obtained from the original model of neuron activity by using randomly switching sequence as an external stimulus. Despite the fact that the values of the external stimulus are selected from a set corresponding to the tonic spiking mode, the blinking model exhibits bursting activity. For both systems, we analyze changes in the dynamical behavior as the period of stochastic switching increases. Using a numerical approximation of the invariant measures of the blinking and averaged systems, we give estimates of a non-stationary and ghost attractors' proximity.Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others' opinions shared on a communication channel and observe others' actions through an influence channel; these interactions determine a two-layer network structure. We offer an application of the proposed framework by tailoring it to study the adoption of a novel social norm, demonstrating that the model is able to capture the emergence of several real-world collective phenomena such as paradigm shifts and unpopular norms. Through the establishment of analytical conditions and Monte Carlo numerical simulations, we shed light on the role of the coupling between opinion dynamics and decision-making, and of the network structure, in shaping the emergence of complex collective behavior in social systems.We consider diffusively coupled heteroclinic networks, ranging from two coupled heteroclinic cycles to small numbers of heteroclinic networks, each composed of two connected heteroclinic cycles. In these systems, we analyze patterns of synchronization as a function of the coupling strength. We find synchronized limit cycles, slowing-down states, as well as quasiperiodic motion of rotating tori solutions, transient chaos, and chaos, in general along with multistable behavior.  https://www.selleckchem.com/products/FK-506-(Tacrolimus).html  This means that coupled heteroclinic networks easily come in disguise even when they constitute the main building blocks of the dynamics. The generated spatial patterns are rotating waves with on-site limit cycles and perturbed traveling waves from on-site quasiperiodic behavior. The bifurcation diagrams of these simple systems are in general quite intricate.In this paper, the alignment of covariant Lyapunov vectors is used to train multi-layer perceptron ensembles in order to predict the duration of regimes in chaotic time series of Rikitake's geomagnetic dynamo model. The machine learning procedure reveals the relevance of the alignment of distinct covariant Lyapunov vectors for the predictions. To train multi-layer perceptron, we use a classification procedure that associates the number of maxima (or minima) inside regimes of motion with the duration of the corresponding regime. Remarkably accurate predictions are obtained, even for the longest regimes whose duration times are around 17.5 Lyapunov times. We also found long duration regimes with a distinctive statistical behavior, namely, the longest regimes are more likely to occur, a quite unusual behavior. In fact, we observed a largest regime above which no regimes were observed.Cardiac alternans is a proarrhythmic state in which the action potential duration (APD) of cardiac myocytes alternate between long and short values and often occurs under conditions of rapid pacing of cardiac tissue. In the ventricles, alternans is especially dangerous due to the life-threatening risk of developing arrhythmias, such as ventricular fibrillation. Alternans can be formed in periodically paced tissue as a result of pacing itself. Recently, it has been demonstrated that this pacing-induced alternans can be prevented by performing constant diastolic interval (DI) pacing, in which DI is independent of APD. However, constant DI pacing is difficult to implement in experimental settings since it requires the real-time measurement of APD. A more practical way was proposed based on electrocardiograms (ECGs), which give an indirect measure of the global DI relaxation period through the TR interval assessment. Previously, we demonstrated that constant TR pacing prevented alternans formation in isolated Langendorff-perfused rabbit hearts.