Delayed Feedback Control Research Articles

Stabilisation with general decay rate by delay feedback control for nonlinear neutral stochastic functional differential equations with infinite delay

Stabilisation with general decay rate by delay feedback control for nonlinear neutral stochastic functional differential equations with infinite delay

Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme

Small-world networks have been of increasing interest because of their high similarity with complex networks in reality. Achievements about controlling the propagation and evolution of small world networks have been highlighted, but little is known about the tipping mechanism and control of such network. In this paper, a novel dynamic delayed feedback scheme is put forward and applied to successfully control the tipping phenomenon in small-world networks. Firstly, the linear characteristic equation of the controlled system is analyzed and the conditions for stability and the occurrence of bifurcation-induced tipping are given. Then, the direction of Hopf bifurcation, which reveals the further evolution mechanism of tipping, is analyzed by using the normal form theory and center manifold reduction. Finally, the numerical simulations are provided to support the theoretical analysis and to verify the effectiveness of the proposed dynamic delayed feedback controller for the small-world network.

Complexity and chaos control of dynamic evolution in energy vehicle production decisions

This study aims to build a dynamic evolutionary game model for production decisions related to new energy vehicles and traditional fuel vehicles under a dual credit policy. The equilibrium point is calculated, and its stability is evaluated. Meanwhile, the dynamic evolution process of the system is simulated numerically, and the results reveal the complexity of the evolution process. Finally, the delay feedback control method is used to suppress the chaos of the model. Results show that in the production competition of duopoly automobile enterprises, automobile enterprises react too quickly to the market, thus resulting in system imbalance and chaos. At the same time, new energy vehicles are more sensitive to the market than traditional fuel vehicles. An excessively large output adjustment speed is not conducive to the smooth transformation of the automobile market. In addition, the delay feedback control method can effectively suppress the chaos in the system. The larger the delay feedback parameter, the faster the system returns to a steady state. This result suggests that policymakers should reflexively use this approach in practice.

Stabilization of differently structured hybrid neutral stochastic systems by delay feedback control under highly nonlinear condition

This paper mainly studies the stabilization of differently structured highly nonlinear hybrid neutral stochastic systems by delay feedback control. Based on the existing works, our new neutral type stochastic system has completely different highly nonlinear structures in switching subspaces, which is more general and applicable. When such a system is given unstable, we focus on studying the asymptotic and exponential stability criteria by designing a feedback control with a time delay for the underlying system. A simulating example is shown to illustrate the feasibility of these results.

Synchronous Control of Neutral Stochastic Neural Network with Discrete and Distributed Delays Based on Delay Feedback Controller

Synchronous Control of Neutral Stochastic Neural Network with Discrete and Distributed Delays Based on Delay Feedback Controller

Asymptotic stability of stochastic differential equations driven by G-Lévy process with delay feedback control

Given an unstable stochastic differential equations, the stabilisation by delay feedback controls for such equations under Lipschitz conditions or highly nonlinear conditions have been discussed by several authors. However, there is few works on the stabilisation by delay feedback controls under the sub-linear expectation associated with a G-L?vy process. The aim of this paper is to design delay feedback controls in the drift part and obtain the asymptotical stability in mean square and quasi-surely asymptotical stability for the stochastic differential equations driven by G-L?vy process with the polynomial growth condition. Lastly, we give an example to verify the obtained theory.

Stability and Hopf bifurcation analysis of a fractional-order ring-hub structure neural network with delays under parameters delay feedback control.

In this paper, a fractional-order two delays neural network with ring-hub structure is investigated. Firstly, the stability and the existence of Hopf bifurcation of proposed system are obtained by taking the sum of two delays as the bifurcation parameter. Furthermore, a parameters delay feedback controller is introduced to control successfully Hopf bifurcation. The novelty of this paper is that the characteristic equation corresponding to system has two time delays and the parameters depend on one of them. Selecting two time delays as the bifurcation parameters simultaneously, stability switching curves in $ (\tau_{1}, \tau_{2}) $ plane and crossing direction are obtained. Sufficient criteria for the stability and the existence of Hopf bifurcation of controlled system are given. Ultimately, numerical simulation shows that parameters delay feedback controller can effectively control Hopf bifurcation of system.

Exploration and Control of Bifurcation in a Fractional-Order Delayed Glycolytic Oscillator Model

Recently, establishing proper dynamical models to describe the relationship among different chemical substances has become a vital theme in chemistry. In this present article, we set up a new fractional-order delayed glycolytic oscillator model. Utilizing the contraction mapping theorem, we explore the existence and uniqueness of the solution to the involved fractional glycolytic oscillator model with delay. By virtue of some suitable analytical skills, we discuss the non-negativeness of the solution to the established fractional glycolytic oscillator system. Taking advantage of a suitable function, we investigate the boundedness of the fractional glycolytic oscillator system. Exploiting the stability and bifurcation theory of fractional dynamical system, we study the stability and the generation of Hopf bifurcation of the fractional glycolytic oscillator system with delay. Making use of delayed feedback controller and PDα controller, we deal with the Hopf bifurcation control of the fractional glycolytic oscillator system owing delay. Computer simulation results are displayed to support the obtained assertions. The acquired results of this article own great theoretical value in dominating the concentrations of different chemical compositions.

Large-Scale Solar PV Converter based Robust Wide-Area Damping Controller for Critical Low Frequency Oscillations in Power Systems

Integration of large-scale renewable energy sources in legacy power system has negative impact on inertia and low-frequency oscillations (LFOs). Critical LFO modes are the primary concern in system stability as they limit the power transfer capability in inter-region tie-lines. Therefore, to provide adequate damping to critical LFO modes, a robust wide-area damping controller (WADC) design is required. In this paper, time delayed feedback control (TDFC) based WADC design is carried out with large-scale solar photovoltaic (SPV). In the design process, geometric technique is used to determine the appropriate wide-area signals. Time delays and noises in feedback signals as well as different operating scenarios have severe implications on the damping performance of WADC. Hence, considering these uncertainties, the proposed WADC parameters are tuned by modified particle swarm optimization (PSO) algorithm. The performance of proposed WADC is demonstrated on SPV-integrated IEEE 4-machine 11-bus and 16-machine 68-bus systems. Critical modes of the system are damped by more than 10 % damping ratio in both cases. Furthermore, nonlinear dynamic simulations demonstrate that the proposed WADC provides robust performance over wide operating scenarios. Finally, practical efficacy of the proposed method is established by experimental validation through real-time simulation using OPAL-RT.

Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay

<abstract><p>Recently, delayed dynamical model has witnessed a great interest from many scholars in biological and mathematical areas due to its potential application in describing the interaction of different biological populations. In this article, relying the previous studies, we set up two new predator-prey systems incorporating delay. By virtue of fixed point theory, inequality tactics and an appropriate function, we explore well-posedness (includes existence and uniqueness, boundedness and non-negativeness) of the solution of the two formulated delayed predator-prey systems. With the aid of bifurcation theorem and stability theory of delayed differential equations, we gain the parameter conditions on the emergence of stability and bifurcation phenomenon of the two formulated delayed predator-prey systems. By applying two controllers (hybrid controller and extended delayed feedback controller) we can efficaciously regulate the region of stability and the time of occurrence of bifurcation phenomenon for the two delayed predator-prey systems. The effect of delay on stabilizing the system and adjusting bifurcation is investigated. Computer simulation plots are provided to sustain the acquired prime outcomes. The conclusions of this article are completely new and can provide some momentous instructions in dominating and balancing the densities of predator and prey.</p></abstract>

Delayed feedback control of PSJA for heat source cooling in a closed space

Delayed feedback control of PSJA for heat source cooling in a closed space

Bifurcation Analysis of a Neutrophil Periodic Oscillation Model with State Feedback Control

The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cells and the circulating neutrophil phase is set forth after delay feedback control of the state variable of stem cells. Hopf bifurcation is discussed with varying free parameters and time delays. Based on the center manifold theory, the normal form near the critical point is computed and the stability of bifurcating periodical solution is rigorously discussed. With the aids of the artificial tool on-hand which implies how much tedious work doing by DDE-Biftool software, the bifurcating periodic solution after Hopf point is continued by varying time delay.

Periodical Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control

The delay feedback control brings forth interesting periodical oscillation bifurcation phenomena which reflect in Mackey-Glass white blood cell model. Hopf bifurcation is analyzed and the transversal condition of Hopf bifurcation is given. Both the period-doubling bifurcation and saddle-node bifurcation of periodical solutions are computed since the observed floquet multiplier overpass the unit circle by DDE-Biftool software in Matlab. The continuation of saddle-node bifurcation line or period-doubling curve is carried out as varying free parameters and time delays. Two different transition modes of saddle-node bifurcation are discovered which is verified by numerical simulation work with aids of DDE-Biftool.

Stabilisation in distribution by delay feedback controls for hybrid stochastic delay differential equations

This article aims to design a linear delay feedback control to stabilise an unstable hybrid stochastic delay differential equation in distribution. Under the global Lipschitz condition, sufficient criteria are established to guarantee the stability of the controlled system. Then LMI techniques are employed to design the control law in two structure forms: state feedback and output injection.

Bifurcation Phenomenon and Control Technique in Fractional BAM Neural Network Models Concerning Delays

In this current study, we formulate a kind of new fractional BAM neural network model concerning five neurons and time delays. First, we explore the existence and uniqueness of the solution of the formulated fractional delay BAM neural network models via the Lipschitz condition. Second, we study the boundedness of the solution to the formulated fractional delayed BAM neural network models using a proper function. Third, we set up a novel sufficient criterion on the onset of the Hopf bifurcation stability of the formulated fractional BAM neural network models by virtue of the stability criterion and bifurcation principle of fractional delayed dynamical systems. Fourth, a delayed feedback controller is applied to command the time of occurrence of the bifurcation and stability domain of the formulated fractional delayed BAM neural network models. Lastly, software simulation figures are provided to verify the key outcomes. The theoretical outcomes obtained through this exploration can play a vital role in controlling and devising networks.

Stabilization of Highly Nonlinear Hybrid Stochastic Differential Delay Equations with Lévy Noise by Delay Feedback Control

Stabilization of Highly Nonlinear Hybrid Stochastic Differential Delay Equations with Lévy Noise by Delay Feedback Control

Dynamic Game of the Dual-Channel Supply Chain Under a Carbon Subsidy Policy

This study investigates the dynamic game behaviors of dual-channel supply chains involving an oligopoly manufacturer selling low-carbon products to online and offline retailers. The price game models under government subsidy are discussed under three scenarios: (1) simultaneous decision, (2) manufacturer dominates the market, and (3) retailer dominates the market. The equilibrium strategies are compared under the government subsidy policy. Using numerical simulation, complex characteristics of the dual-channel supply chain under the carbon subsidy policy are investigated. The complexity of wholesale price and sales commission of each channel are analyzed by bifurcation, largest Lyapunov exponent and basin of attraction diagrams. Furthermore, parameter adjustment and delayed feedback control methods are proven to be effective approaches to chaos control.

Size effects of the nonlinear resonance analysis of a microbeam under time delay feedback control

Size effects of the nonlinear resonance analysis of a microbeam under time delay feedback control

Stabilization of highly nonlinear hybrid systems driven by Lévy noise and delay feedback control based on discrete-time state observations

There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.

Stability, co-dimension two bifurcations and chaos control of a host-parasitoid model with mutual interference

In host-parasitiod models, it is widely accepted that mutual interference of parasitoids has stabilizing effect. Conversely, parasitoids interference might significantly destabilize host-parasitoid model dynamics as well. To characterize such dynamics, a host-parasitoid model with mutual interference is investigated. First, we examine the uniformly boundedness of the present model solutions. Then, the existence and uniqueness of the positive fixed point are discussed. Moreover, the parametric conditions of the positive fixed point stability are derived. Besides, we explored the bifurcation behaviors involving 1:2 resonance, 1:3 resonance and 1:4 resonance using normal form approach of discrete-time models and bifurcation theory. In this method, it is not required to switch into Jordan form and compute the center manifold approximation of the present map. It is sufficient to calculate the critical non-degeneracy coefficients to check the listed bifurcation types. Furthermore, the state delayed feedback control technique is applied to regulate the chaotic behaviors of the model. Finally, numerical simulations are provided to support our theoretical results.