This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can em...This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.For the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors.展开更多
An adaptive state feedback predictive control （SFPC） scheme and an expert control scheme are presented and applied to the temperature control of a 1200 kt·a^-1 delayed coking furnace, which is the key equipment...An adaptive state feedback predictive control （SFPC） scheme and an expert control scheme are presented and applied to the temperature control of a 1200 kt·a^-1 delayed coking furnace, which is the key equipment for the delayed coking process. Adaptive SFPC is used to improve the performance of temperature control in normal operation. A simplified nonlinear model on the basis of first principles of the furnace is developed to obtain a state space model by linearization. Taking advantage of the nonlinear model, an online model adapting method is presented to accommodate the dynamic change of process characteristics because of tube coking and load changes. To compensate the large inverse response of outlet temperature resulting from the sudden increase of injected steam of a particular velocity to tubes, a monitoring method and an expert control scheme based on heat balance calculation are proposed. Industrial implementation shows the effectiveness and feasibility of the proposed control strategy.展开更多
An autapse is an unusual synapse that occurs between the axon and the soma of the same neuron. Mathematically, it can be described as a self-delayed feedback loop that is defined by a specific time-delay and the so-ca...An autapse is an unusual synapse that occurs between the axon and the soma of the same neuron. Mathematically, it can be described as a self-delayed feedback loop that is defined by a specific time-delay and the so-called autaptic coupling strength. Recently, the role and function of autapses within the nervous system has been studied extensively. Here, we extend the scope of theoretical research by investigating the effects of an autapse on the transmission of a weak localized pacemaker activity in a scale-free neuronal network. Our results reveal that by mediating the spiking activity of the pacemaker neuron, an autapse increases the propagation of its rhythm across the whole network, if only the autaptic time delay and the autaptic coupling strength are properly adjusted. We show that the autapse-induced enhancement of the transmission of pacemaker activity occurs only when the autaptic time delay is close to an integer multiple of the intrinsic oscillation time of the neurons that form the network. In particular, we demonstrate the emergence of multiple resonances involving the weak signal, the intrinsic oscillations, and the time scale that is dictated by the autapse. Interestingly, we also show that the enhancement of the pacemaker rhythm across the network is the strongest if the degree of the pacemaker neuron is lowest. This is because the dissipation of the localized rhythm is contained to the few directly linked neurons, and only afterwards, through the secondary neurons, it propagates further. If the pacemaker neuron has a high degree, then its rhythm is simply too weak to excite all the neighboring neurons, and propagation therefore fails.展开更多
Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is propos...Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is proposed to suppress vibration of the primary system under excitation with changing frequency. Firstly, the mechanical model of the delay coupled system is established. Then, the displacement transfer ratio of the system is obtained. The stability of the system is analyzed since delay may result in destabilization. Next, in order to design the control parameters, the vibration absorption performances of the proposed time-delayed vibration absorber are studied. The vibration absorption region is shown. The results show that time-delayed feedback control is able to change the response of the system. The effective vibration absorption frequency band is adjustable by tuning the control gain and time delay. The effective frequency band can be widened when choosing appropriate control parameters. The vibration absorption performances can be greatly improved by the time-delayed absorber. In addition, the optimum control parameters are obtained. Finally, the experimental prototype is constructed. Several tests with different control parameters are taken. The experimental and analytical results match quite well.展开更多
Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are ...Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.展开更多
This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting eff...This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.展开更多
In this paper,a new delayed fractional-order model including susceptible migratory birds,infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds.Fear of predators is ...In this paper,a new delayed fractional-order model including susceptible migratory birds,infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds.Fear of predators is considered in the model,as fear can reduce the reproduction rate and disease transmission rate among prey.First,some basic mathematical results of the proposed model are discussed.Then,time delay is regarded as a bifurcation parameter,and the delay-induced bifurcation conditions for such an uncontrolled system are established.A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon.It is found that the control scheme can successfully suppress the bifurcation behavior of the system,and the pulse width can be arbitrarily selected on the premise of ensuring the control effect.Compared with the traditional time-delay feedback controller,the control scheme proposed in this paper has more advantages in practical application,which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment.The proposed control scheme,in particular,remains effective even after the system has been disrupted by a constant.Numerical simulation verifies the correctness of the theoretical results.展开更多
The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The fi...The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.110020731117201711102041)
文摘This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.For the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors.
基金the State Key Development Program for Basic Research of China(2002CB312200)the National High Technology Research and Development Program of China(2007AA04Z193)
文摘An adaptive state feedback predictive control （SFPC） scheme and an expert control scheme are presented and applied to the temperature control of a 1200 kt·a^-1 delayed coking furnace, which is the key equipment for the delayed coking process. Adaptive SFPC is used to improve the performance of temperature control in normal operation. A simplified nonlinear model on the basis of first principles of the furnace is developed to obtain a state space model by linearization. Taking advantage of the nonlinear model, an online model adapting method is presented to accommodate the dynamic change of process characteristics because of tube coking and load changes. To compensate the large inverse response of outlet temperature resulting from the sudden increase of injected steam of a particular velocity to tubes, a monitoring method and an expert control scheme based on heat balance calculation are proposed. Industrial implementation shows the effectiveness and feasibility of the proposed control strategy.
文摘An autapse is an unusual synapse that occurs between the axon and the soma of the same neuron. Mathematically, it can be described as a self-delayed feedback loop that is defined by a specific time-delay and the so-called autaptic coupling strength. Recently, the role and function of autapses within the nervous system has been studied extensively. Here, we extend the scope of theoretical research by investigating the effects of an autapse on the transmission of a weak localized pacemaker activity in a scale-free neuronal network. Our results reveal that by mediating the spiking activity of the pacemaker neuron, an autapse increases the propagation of its rhythm across the whole network, if only the autaptic time delay and the autaptic coupling strength are properly adjusted. We show that the autapse-induced enhancement of the transmission of pacemaker activity occurs only when the autaptic time delay is close to an integer multiple of the intrinsic oscillation time of the neurons that form the network. In particular, we demonstrate the emergence of multiple resonances involving the weak signal, the intrinsic oscillations, and the time scale that is dictated by the autapse. Interestingly, we also show that the enhancement of the pacemaker rhythm across the network is the strongest if the degree of the pacemaker neuron is lowest. This is because the dissipation of the localized rhythm is contained to the few directly linked neurons, and only afterwards, through the secondary neurons, it propagates further. If the pacemaker neuron has a high degree, then its rhythm is simply too weak to excite all the neighboring neurons, and propagation therefore fails.
基金the National Natural Science Foundation of China (Grants 11572224 and 11772229).
文摘Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is proposed to suppress vibration of the primary system under excitation with changing frequency. Firstly, the mechanical model of the delay coupled system is established. Then, the displacement transfer ratio of the system is obtained. The stability of the system is analyzed since delay may result in destabilization. Next, in order to design the control parameters, the vibration absorption performances of the proposed time-delayed vibration absorber are studied. The vibration absorption region is shown. The results show that time-delayed feedback control is able to change the response of the system. The effective vibration absorption frequency band is adjustable by tuning the control gain and time delay. The effective frequency band can be widened when choosing appropriate control parameters. The vibration absorption performances can be greatly improved by the time-delayed absorber. In addition, the optimum control parameters are obtained. Finally, the experimental prototype is constructed. Several tests with different control parameters are taken. The experimental and analytical results match quite well.
基金Project supported by the National Natural Science Foundation of China (Grant No.12072025)the Beijing Natural Science Foundation (Grant No.1222015)。
文摘Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11902081)the Science and Technology Projects of Guangzhou (Grant No. 202201010326)the Guangdong Provincial Basic and Applied Basic Research Foundation (Grant No. 2023A1515010833)。
文摘This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.
基金supported by Liaoning Provincial Department of Education Scientific Research Fund Project(lnjc202018).
文摘In this paper,a new delayed fractional-order model including susceptible migratory birds,infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds.Fear of predators is considered in the model,as fear can reduce the reproduction rate and disease transmission rate among prey.First,some basic mathematical results of the proposed model are discussed.Then,time delay is regarded as a bifurcation parameter,and the delay-induced bifurcation conditions for such an uncontrolled system are established.A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon.It is found that the control scheme can successfully suppress the bifurcation behavior of the system,and the pulse width can be arbitrarily selected on the premise of ensuring the control effect.Compared with the traditional time-delay feedback controller,the control scheme proposed in this paper has more advantages in practical application,which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment.The proposed control scheme,in particular,remains effective even after the system has been disrupted by a constant.Numerical simulation verifies the correctness of the theoretical results.
基金Project supported by the National Natural Science Foundation of China (Nos. 12122208, 11972254,and 11932015)。
文摘The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.
