Bifurcation analysis and application for impulsive systems with delayed impulses

Electronic version of an article published in International Journal of Bifurcation and Chaos, Volume 27, Issue 12, November 2017, 1750186 [23 pages]. DOI: 10.1142/S0218127417501863, © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ijbcIn this article, we present a systematic approach to bifurcation analysis of impulsive systems with autonomous or periodic right-hand sides that may exhibit delayed impulse terms. Methods include Lyapunov–Schmidt reduction and center manifold reduction. Both methods are presented abstractly in the context of the stroboscopic map associated to a given impulsive system, and are illustrated by way of two in-depth examples: the analysis of a SIR model of disease transmission with seasonality and unevenly distributed moments of treatment, and a scalar logistic differential equation with a delayed census impulsive harvesting effort. It is proven that in some special cases, the logistic equation can exhibit a codimension two bifurcation at a 1:1 resonance point

Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals

In this Letter the issue of impulsive Synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective. (C) 2009 Elsevier Ltd. All rights reserved

Impulsive control of nonlinear systems with impulse time window and bounded gain error

In this paper, we establish a new sufficient condition for the stability of impulsive systems with impulse time window and bounded gain error. The proposed result is more general and more applicable than some existing results. Finally, a numerical example is given to show the effectiveness of our result

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Bi-directional impulse chaos control in crystal growth

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Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

Impulsive Goodwin’s Oscillator Model of Endocrine Regulation: Local Feedback Leads to Multistability

The impulsive Goodwin’s oscillator (IGO) is a hybrid model that captures complex dynamics arising in continuous systems controlled by pulse-modulated (event-based) feedback. Being conceived to describe pulsatile endocrine regulation, it has also found applications in e.g. pharmacokinetics. The original version of the IGO assumes the continuous part of the model to be a chain of first-order blocks. This paper explores the nonlinear phenomena arising due to the introduction of a local continuous feedback as suggested by the endocrine applications. The effects caused by a nonlinear feedback law parameterized by a Hill function are compared to those arising due to a simpler and previously treated case of affine feedback law. The hybrid dynamics of the IGO are reduced to a (discrete) Poincaré map governing the propagation of the model’s continuous states through the firing instants of the impulsive feedback. Bifurcation analysis of the map reveals in particular that both the local Hill function and affine feedback can lead to multistability, which phenomenon has not been observed in the usual IGO model

Exponential Synchronization of Stochastic Complex Dynamical Networks with Impulsive Perturbations and Markovian Switching

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist of κ modes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employing M-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results