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The issue of impulsive control theory for synchronization of the MCK circuit is developed. We propose an impulsive control scheme for the complete synchronization of the MCK circuit including chaotic systems. A sufficient condition for the impulsive control is derived, with an easily calculated maximum impulsive interval. The proposed impulsive control scheme is applied to the MCK circuit and the simulation result demonstrates the effectiveness of the method.

The issue of impulsive synchronization of the coupled chaotic laser plasma system is investigated. A new framework for impulsive synchronization of such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. We derive some sufficient conditions for the synchronization of a laser plasma system via impulsive control with the varying impulsive intervals, which allows us to derive the impulsive synchronization law easily. To illustrate the effectiveness of the proposed results, two numerical examples are given.

This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear Rossler chaotic systems and the simulation results demonstrate the effectiveness of the method.

In recent years,the modeling and application of biological neurons have gained more and more attention.By now, the research on neuron models has become one of the most important branches of neuroscience.Neuron models can be used in various areas,such as biomimetic applications,memory design,logical computing,and signal processing. Furthermore,it is significant to study the dynamic characteristics of neural system by using neuron models.In this paper,the historical development of neuron models is reviewed.The neuron models have experienced three development stages.In the pioneering stage,a group of scientists laid the experimental and theoretical foundation for later research. Then,the whole study started to blossom after the publication of Hodgkin-Huxley model.In the 1970s and 1980s,various models were proposed.One of the research focuses was the simulation of neural repetitive spiking.Since the 1990s, researchers have paid more attention to setting up models that are both physiologically meaningful and computationally effective.The model put forward by Izhikevich E M has been proved to solve the problem successfully.Recently,IBM presented a versatile spiking neuron model based on 1272 ASIC gates.The model,both theoretically understandable and physically implementable,has been used as a basic building block in IBM's neuro-chip TrueNorth.In the paper, seventeen neuron models worth studying are listed.To give a more explicit explanation,these models are classified as two groups,namely conductance-dependent and conductance-independent models.The former group's goal is to model the electrophysiology of neuronal membrane,while the latter group is only to seek for capturing the input-output behavior of a neuron by using simple mathematical abstractions.The complexity and features of each model are illustrated in a chart,while the prominent repetitive spiking curves of each model are also exhibited.Five of the models are further detailed,which are the Hodgkin-Huxley model,the Integrate-and-fire model,the Fitzhugh-Nagumo model,the Izhikevich model,and the most recent model used by IBM in its neuro-chip TrueNorth.Finally,three questions are put forward at the end of the paper,which are the most important problems that today's researchers must consider when setting up new neuron models.In conclusion,the feasibility of physical implementation remains to be a challenge to all researchers. Through the aforementioned work,the authors aim to provide a reference for the study that follows,helping researchers to compare those models in order to choose the properest one.