It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual...It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.展开更多
Ignition delay times of China No.3 aviation kerosene were measured behind reflected shock waves using a heated high-pressure shock tube.Experimental conditions covered a wider temperature range of 820-1500 K,at pressu...Ignition delay times of China No.3 aviation kerosene were measured behind reflected shock waves using a heated high-pressure shock tube.Experimental conditions covered a wider temperature range of 820-1500 K,at pressures of 5.5,11 and 22 atm,equivalence ratios of 0.5,1.0 and 1.5,and oxygen concentration of 20%.Adsorption of kerosene on the shock tube wall was taken into account.Ignition delay times were determined from the onset of the excited radical OH emission in conjunction with the pressure profiles.The experimental results of ignition delay time were correlated with the equations:11 0.22 1.09 2 3.2 10 [Keros ene ] [O2] exp(69941 RT) and 7 0.88 0.23 4.72 10 P exp(62092 RT).The current measurements provide the ignition delay behavior of China No.3 aviation kerosene at high pressures and air-like O2 concentration.展开更多
Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent pre...Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.展开更多
A delayed predator-prey diffusion system with homogeneous Neumann boundary condi- tion is considered. In order to study the impact of the time delay on the stability of the model, the delay ^- is taken as the bifurcat...A delayed predator-prey diffusion system with homogeneous Neumann boundary condi- tion is considered. In order to study the impact of the time delay on the stability of the model, the delay ^- is taken as the bifurcation parameter, the results show that when the time delay across some critical values, the Hopf bifurcations may occur. In particular, by using the normal form theory and the center manifold reduction for partial functional differential equations, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solution have been established. The effect of the diffusion on the bifurcated periodic solution is also considered. A numerical example is given to support the main result.展开更多
In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the ...In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.展开更多
In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple ...In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.展开更多
文摘It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.
基金supported by the National Natural Science Foundation of China (Grant No.90916017)
文摘Ignition delay times of China No.3 aviation kerosene were measured behind reflected shock waves using a heated high-pressure shock tube.Experimental conditions covered a wider temperature range of 820-1500 K,at pressures of 5.5,11 and 22 atm,equivalence ratios of 0.5,1.0 and 1.5,and oxygen concentration of 20%.Adsorption of kerosene on the shock tube wall was taken into account.Ignition delay times were determined from the onset of the excited radical OH emission in conjunction with the pressure profiles.The experimental results of ignition delay time were correlated with the equations:11 0.22 1.09 2 3.2 10 [Keros ene ] [O2] exp(69941 RT) and 7 0.88 0.23 4.72 10 P exp(62092 RT).The current measurements provide the ignition delay behavior of China No.3 aviation kerosene at high pressures and air-like O2 concentration.
文摘Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.
文摘A delayed predator-prey diffusion system with homogeneous Neumann boundary condi- tion is considered. In order to study the impact of the time delay on the stability of the model, the delay ^- is taken as the bifurcation parameter, the results show that when the time delay across some critical values, the Hopf bifurcations may occur. In particular, by using the normal form theory and the center manifold reduction for partial functional differential equations, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solution have been established. The effect of the diffusion on the bifurcated periodic solution is also considered. A numerical example is given to support the main result.
基金Supported by Research Project of Hubei Provincial Department of Education under Grant No. Q20101609Foundation of Wuhan Textile University under Grant No. 105040
文摘In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.
文摘In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.
