This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system. First, it is found that there exist five equilibria in the chaotic system, and the stabilities of these equili...This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system. First, it is found that there exist five equilibria in the chaotic system, and the stabilities of these equilibria are discussed under a constant scalar control input parameter m. Secondly, the trajectories of the attractors on a y-z plane are examined, the reasons why these trajectories can exist or disappear are also described. Finally, the forming procedure of the different scrolls chaotic attractor is explored by computer simulations when the parameter m is varied. It is shown that the new chaotic attractor has a compound structure, it can evolve to other three-dimensional autonomous chaotic systems. The results of theoretical analysis and simulation are helpful for better understanding of other similar chaotic systems.展开更多
Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the firs...Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabi1ize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the origina1 system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.展开更多
In this paper, a strongly coupled diffusive predator-prey system with a modified Leslie- Gower term is considered. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotica...In this paper, a strongly coupled diffusive predator-prey system with a modified Leslie- Gower term is considered. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create stationary patterns.展开更多
The study aims to evaluate the potential of GHG （greenhouse gas） reductions by installing an anaerobic digester in a wastewater treatment facility in Southeast Asia. Then the break-even point of additional investmen...The study aims to evaluate the potential of GHG （greenhouse gas） reductions by installing an anaerobic digester in a wastewater treatment facility in Southeast Asia. Then the break-even point of additional investment to reduce GHG is obtained by exchanging carbon price as emissions credits. In the project scenario, the wastewater treatment system has the digester, where methane （biogas） is produced and recovered. Compared with the baseline scenario, the biogas has calorific value to produce heat and electricity, and can substitute fossil fuels for power generation. The objective of the study is to define the relationship between CERs （certified emission reductions） and investment costs, and the beak-even point, finding out the dominant pa- rameters in the system. Financial parameters such as capital costs and operating costs are considered to evaluate the investmerit costs. The result shows that the methane recovery reduces 54% of GHG emissions. Although the substitution of the biogas for the fossil fuels reduces only 6% of the GHG emissions, the electricity output can satisfy the electricity consumption. The results also show that the maximum CER credit is 73000 t-COEe/a, and the GHG reduction cost is 14 USD/t-CO2e.展开更多
A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticidetreate...A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticidetreated bed-nets usage. The occurrence of a backward bifurcation at R0 = 1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic repro- duction number is less than unity. This phenomenon is found to be caused by disease- induced human mortality. The global asymptotic stability of the endemic equilibrium for R0 〉1 is proved, by using the geometric method for global stability. Therefore, the disease becomes endemic for R0〉 1 regardless of the number of initial cases in both the human and vector populations. Finally, the impact on system dynamics of vector＇s host preferences and bed-net usage behavior is investigated.展开更多
A stochastic predator prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In additi...A stochastic predator prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In addition, conditions of global stability for the determin- istic system are also established from the above result. By Lyapunov function, the long time behavior of solution around the disease-free equilibrium of deterministic system is derived. These results mean that stochastic system has the similar property with the corresponding deterministic system. When the white noise is small, however, large envi- ronmental noise makes the result different. Finally, numerical simulations are carried out to support our findings.展开更多
In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium t...In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium to a reaction^diffusion system with homo- geneous Neumann boundary conditions is considered. Sufficient conditions for the local and global asymptotic stability are given by linearization and the method of upper and lower solutions and its associated monotone iterations. The result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.展开更多
文摘This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system. First, it is found that there exist five equilibria in the chaotic system, and the stabilities of these equilibria are discussed under a constant scalar control input parameter m. Secondly, the trajectories of the attractors on a y-z plane are examined, the reasons why these trajectories can exist or disappear are also described. Finally, the forming procedure of the different scrolls chaotic attractor is explored by computer simulations when the parameter m is varied. It is shown that the new chaotic attractor has a compound structure, it can evolve to other three-dimensional autonomous chaotic systems. The results of theoretical analysis and simulation are helpful for better understanding of other similar chaotic systems.
文摘Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabi1ize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the origina1 system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.
文摘In this paper, a strongly coupled diffusive predator-prey system with a modified Leslie- Gower term is considered. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create stationary patterns.
文摘The study aims to evaluate the potential of GHG （greenhouse gas） reductions by installing an anaerobic digester in a wastewater treatment facility in Southeast Asia. Then the break-even point of additional investment to reduce GHG is obtained by exchanging carbon price as emissions credits. In the project scenario, the wastewater treatment system has the digester, where methane （biogas） is produced and recovered. Compared with the baseline scenario, the biogas has calorific value to produce heat and electricity, and can substitute fossil fuels for power generation. The objective of the study is to define the relationship between CERs （certified emission reductions） and investment costs, and the beak-even point, finding out the dominant pa- rameters in the system. Financial parameters such as capital costs and operating costs are considered to evaluate the investmerit costs. The result shows that the methane recovery reduces 54% of GHG emissions. Although the substitution of the biogas for the fossil fuels reduces only 6% of the GHG emissions, the electricity output can satisfy the electricity consumption. The results also show that the maximum CER credit is 73000 t-COEe/a, and the GHG reduction cost is 14 USD/t-CO2e.
文摘A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticidetreated bed-nets usage. The occurrence of a backward bifurcation at R0 = 1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic repro- duction number is less than unity. This phenomenon is found to be caused by disease- induced human mortality. The global asymptotic stability of the endemic equilibrium for R0 〉1 is proved, by using the geometric method for global stability. Therefore, the disease becomes endemic for R0〉 1 regardless of the number of initial cases in both the human and vector populations. Finally, the impact on system dynamics of vector＇s host preferences and bed-net usage behavior is investigated.
文摘A stochastic predator prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In addition, conditions of global stability for the determin- istic system are also established from the above result. By Lyapunov function, the long time behavior of solution around the disease-free equilibrium of deterministic system is derived. These results mean that stochastic system has the similar property with the corresponding deterministic system. When the white noise is small, however, large envi- ronmental noise makes the result different. Finally, numerical simulations are carried out to support our findings.
基金This work was financially supported by the Natural Science Foundation of China （11271236, 11401356） and the Natural Science Basic Research Plan in Shaanxi Province of China （No. 2015JM1008）.
文摘In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium to a reaction^diffusion system with homo- geneous Neumann boundary conditions is considered. Sufficient conditions for the local and global asymptotic stability are given by linearization and the method of upper and lower solutions and its associated monotone iterations. The result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.
