In the present paper, we study phase waves of self-sustained oscillators with a nearest-neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics, we approximate the lattice with a quasi-continuum (QC). The resulting partial differential model is then further reduced to the Gardner equation, which predicts many properties of the underlying solitary structures. Using an iterative procedure on the original lattice equations, we determine the shapes of solitary waves, kinks, and the flat-like solitons that we refer to as flatons. Direct numerical experiments reveal that the interaction of solitons and flatons on the lattice is notably clean. All in all, we find that both the QC and the Gardner equation predict remarkably well the discrete patterns and their dynamics.In multitask networks, neighboring agents that belong to different clusters pursue different goals, and therefore arbitrary cooperation will lead to a degradation in estimation performance. In this paper, an adaptive clustering method is proposed for distributed estimation that enables agents to distinguish between subneighbors that belong to the same cluster and those that belong to a different cluster.  https://www.selleckchem.com/products/sf2312.html  This creates an appropriate degree of cooperation to improve parameter estimation accuracy, especially for the case where the prior information of a cluster is unknown. In contrast to the static and quantitative threshold that is imposed in traditional clustering methods, we devise a method for real-time clustering hypothesis detection, which is constructed through the use of a reliable adaptive clustering threshold as reference and the averaged element-wise distance between tasks as real-time clustering detection statistic. Meanwhile, we relax the clustering conditions to maintain maximum cooperation without sacrificing accuracy. Simulations are presented to compare the proposed algorithm and some traditional clustering strategies in both stationary and nonstationary environments. The effects of task difference on performance are also obtained to demonstrate the superiority of our proposed clustering strategy in terms of accuracy, robustness, and suitability.We report a new kind of discontinuous spiral with stable periodic orbits in the parameter space of an optically injected semiconductor laser model, which is a combination of the intercalation of fish-like and cuspidal-like structures (the two normal forms of complex cubic dynamics). The spiral has a tridimensional structure that rolls up in at least three directions. A turn of approximately 2π radians along the spiral and toward the center increases the number of peaks in the laser intensity by one, which does not occur when traversing the discontinuities. We show that as we vary the linewidth enhancement factor (α), discontinuities are created (destroyed) through disaggregation (collapses) from (into) the so-called shrimp-like structures. Future experimental verification and applications, as well as theoretical studies to explain its origin and relation with homoclinic spirals that exist in its neighborhood, are needed.In this paper, the harmonic balance method with the alternating frequency/time (HB-AFT) domain technique is extended to the dynamical systems with state-dependent delays and non-smooth right-hand side for the first time. Two types of network congestion control models [the modified transmission control protocol-random early detection (TCP-RED) model and the fluid-flow TCP-additive increase multiplicative decease (AIMD)/RED model] with state-dependent round-trip time delays and non-smooth right-hand side are considered in detail. First, their dynamics and bifurcation are analyzed by the numerical analysis method. Then, the analytical approximate expressions of the periodic solutions are obtained by employing the semi-analytical method named as HB-AFT. The results of the numerical simulation and HB-AFT agree with each other very well. It indicates that the HB-AFT technique is simple, valid, effective, and accurate for the non-smooth dynamical systems with state-dependent time delays. Besides, more complicated ancontrol, which is very important in practical application.This paper proposes a simple locally active memristor whose state equation only consists of linear terms and an easily implementable function and design for its circuit emulator. The effectiveness of the circuit emulator is validated using breadboard experiments and numerical simulations. The proposed circuit emulator has a simple structure, which not only reduces costs but also increases its application value. The power-off plot and DC V-I Loci verify that the memristor is nonvolatile and locally active, respectively. This locally active memristor exhibits low cost, easy physical implementation, and wide locally active region characteristics. Furthermore, a neural model composed of two 2D HR neurons based on the proposed locally active memristor is established. It is found that complicated firing behaviors occur only within the locally active region. A new phenomenon is also discovered that shows coexisting position symmetry for different attractors. The firing pattern transition is then observed via bifurcation analysis. The results of MATLAB simulations are verified from the hardware circuits.Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximization. We propose a stylized model with a history-dependent utility function, where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find, in particular, that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behavior.