共查询到20条相似文献,搜索用时 15 毫秒
1.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(4):1028-1035
In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution. 相似文献
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A turbidostat is an apparatus with feedback control system used to continuously culturing microorganisms. The dilution rate of the turbidostat can be regulated by the control system when the concentration of microorganism, detected by photoelectricity system or other devices, reaches a preset value. Based on the design ideas of the turbidostat, a differential equation with impulsive state feedback control is proposed for a kind of turbidostat system in this paper. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions for the existence of periodic solution of order one are obtained according to the preset value and the types of the positive equilibrium of the corresponding system without impulsive control. Furthermore, it is pointed out that the system either tends to a stable state or has a periodic solution. Finally, the theoretical results are verified by numerical simulations. 相似文献
4.
In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis. 相似文献
5.
A. K. Demenchuk 《Differential Equations》2010,46(10):1389-1394
We consider a linear periodic control system with zero mean of the coefficient matrix and with linear state feedback control
periodic with the same period. We obtain necessary and sufficient conditions for the solvability of the frequency spectrum
control problem with a given goal set for strongly irregular periodic vibrations. In this problem, one should find a feedback
coefficient such that the closed system has a strongly irregular periodic solution with the desired frequencies. 相似文献
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《Chaos, solitons, and fractals》2007,31(2):448-461
The complex dynamics of a Holling type II prey–predator system with impulsive state feedback control is studied in both theoretical and numerical ways. The sufficient conditions for the existence and stability of semi-trivial and positive periodic solutions are obtained by using the Poincaré map and the analogue of the Poincaré criterion. The qualitative analysis shows that the positive periodic solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams, Lyapunov exponents, and phase portraits are illustrated by an example, in which the chaotic solutions appear via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed. 相似文献
8.
Homoclinic Cycle and Homoclinic Bifurcations of
a Predator-prey Model with Impulsive State
Feedback Control 下载免费PDF全文
Tongqian Zhang Tong Xu Junling Wang Zhichao Jiang 《Journal of Nonlinear Modeling and Analysis》2020,2(2):227-240
In this paper, the homoclinic bifurcation of a predator-prey system with impulsive state feedback control is investigated. By using the geometry theory of semi-continuous dynamic systems, the existences of order-1 homoclinic cycle and order-1 periodic solution are obtained. Then the stability of order-1 periodic solution is studied. At last, an example is presented to illustrate the main results. 相似文献
9.
In this paper, we study a predator–prey system with an Ivlev-type functional response and impulsive control strategies containing a biological control (periodic impulsive immigration of the predator) and a chemical control (periodic pesticide spraying) with the same period, but not simultaneously. We find conditions for the local stability of the prey-free periodic solution by applying the Floquet theory of an impulsive differential equation and small amplitude perturbation techniques to the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. Moreover, we add a forcing term into the prey population’s intrinsic growth rate and find the conditions for the stability and for the permanence of this system. 相似文献
10.
A single population growth model with stage‐structured and state‐dependent impulsive control is proposed. By using the Poincar'e map and the analogue of Poincaré's criterion, we prove the existence and the stability of positive order‐1 or order‐2 periodic solution. Moreover, we show that there is no periodic solution with order greater than or equal to three. Numerical results are carried out to illustrate the feasibility of our main results and the superiority of state feedback control strategy is also discussed. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
In this paper, a general Kolmogorov type predator–prey model is considered. Together with a constant-yield predator harvesting, the state dependent feedback control strategies which take into account the impulsive harvesting on predators as well as the impulsive stocking on the prey are incorporated in the process of population interactions. We firstly study the existence of an order-1 homoclinic cycle for the system. It is shown that an order-1 positive periodic solution bifurcates from the order-1 homoclinic cycle through a homoclinic bifurcation as the impulsive predator harvesting rate crosses some critical value. The uniqueness and stability of the order-1 positive periodic solution are derived by applying the geometry theory of differential equations and the method of successor function. Finally, some numerical examples are provided to illustrate the main results. These results indicate that careful management of resources and harvesting policies is required in the applied conservation and renewable resource contexts. 相似文献
12.
Geometrical analysis of a pest management model in food-limited environments with nonlinear impulsive state feedback control 下载免费PDF全文
Tongqian Zhang Tong Xu Junling Wang Yi Song Zhichao Jiang 《Journal of Applied Analysis & Computation》2019,9(6):2261-2277
In this paper, a nonlinear impulsive state feedback control system is proposed to model an integrated pest management in food-limited environments. In the system, impulsive feedback control measures are implemented to control pests on the basis of the quantitative state of pests. Mathematically, an intuitive geometric analysis is used to indicate the existence of periodic solutions. The stability of periodic solutions is investigated by using Analogue of Poincar\''{e} Criterion. At last, numerical simulations are given to verify the theoretical analysis. 相似文献
13.
According to the initial density of a single species with Allee effect and corresponding management strategy, three kinds of mathematical models are presented to describe the evolutionary process of the species by impulsive differential equations. When the initial density of the species is larger than economic injury level (EIL) (or economical threshold, ET), impulsive harvest control is considered in a finite time to decrease the population of the species. The feasibility of the impulsive harvest control in a finite time is given by the existence of solution of the model with initial and boundary value problem. When the initial density of the species is less than EIL (or ET), the model with state feedback control is formulated according to the state of the species. The existence and stability of periodic solution of the model with state feedback control are discussed. When the initial density of the species is less than the Allee threshold and the species tends to extinction, the model with impulsive release at fixed moments is presented to study the restoration of the species. The conditions for the feasibility of periodic restoration of the species are given. Finally, some discussions are given. 相似文献
14.
In this paper, an impulsive periodic predator–prey system with Watt-type functional response is investigated. By using the Floquet theory of linear periodic impulsive equation, the stability conditions for the prey-eradication positive periodic solution are given, and the boundedness of the system is proved. By the method of coincidence degree, the sufficient conditions for the existence of at least one strictly positive periodic solution are obtained. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful for ecosystem control. 相似文献
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In the paper, we investigate an eco-epidemic system with impulsive birth. The conditions for the stability of infection-free periodic solution are given by applying Floquet theory of linear periodic impulsive equation. And we give the conditions of persistence by constructing a consequence of some abstract monotone iterative schemes. By using the method of coincidence degree, a set of sufficient conditions are derived for the existence of at least one strictly positive periodic solution. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels. 相似文献
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Jianmei Wang Huidong Cheng Yan Li Xiaoning Zhang 《Journal of Applied Analysis & Computation》2018,8(2):427-442
Starting from the practical problems of integrated pest management, we establish a predator-prey model for pest control with multi-state dependent impulsive, which adopts two different control methods for two different thresholds. By applying geometry theory of impulsive differential equations and the successor function, we obtain the existence of order one periodic solution. Then the stability of the order one periodic solution is studied by analogue of the Poincar\''{e} criterion. Finally, some numerical simulations are exerted to show the feasibility of the results. 相似文献
17.
The dynamics of a predator–prey model with impulsive state feedback control, which is described by an autonomous system with impulses, is studied. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincaré map and analogue of the Poincaré criterion. The qualitative analysis shows that the positive period-1 solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations. 相似文献
18.
In this paper, the dynamic behaviors of a two-prey two-predator system with impulsive effect on the predator of fixed moment are investigated. By applying the Floquet theory of liner periodic impulsive equation, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we prove that the system is permanent if the impulsive period is large than some critical value, and meanwhile the conditions for the extinction of one of the two prey and permanence of the remaining three species are given. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels. 相似文献
19.
In this paper, we consider a class of nonlinear impulsive delay differential equations. By establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing Banach fixed point theorem, we obtain several sufficient conditions ensuring the existence, uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay differential equations. Furthermore, the criteria are applied to analyze dynamical behavior of impulsive delay Hopfield neural networks and the results show different behavior of impulsive system originating from one continuous system. 相似文献
20.
In this paper, a mathematical model including the phytoplankton and zooplankton with the impulsive feedback control is presented. The sufficient conditions for the existence of the order-1 and order-2 periodic solutions are obtained by using the geometrical theory of semi-continuous dynamic system. The stability of the order-1 periodic solution is discussed by the analogue of the Poincaré criterion. Finally, our results are justified by the numerical simulations. 相似文献