The purpose of this paper is to investigate the macroeconomic effect of pollution emission in an overlapping generation system. This is done through constructing an endogenous economy which generates pollution and env...The purpose of this paper is to investigate the macroeconomic effect of pollution emission in an overlapping generation system. This is done through constructing an endogenous economy which generates pollution and environment deterioration. It shows how different level of pollution emission could cause complexity such as fold bifurcation in this system. In addition, numerical simulations are provided to show the emergency of complexity.展开更多
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 cel...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.展开更多
In this paper, Mira 2 map is investigated. The conditions of the existence for fold bifurcation, flip bifurcation and Naimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. And...In this paper, Mira 2 map is investigated. The conditions of the existence for fold bifurcation, flip bifurcation and Naimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. And the conditions of the existence for chaos in the sense of Marroto are obtained. Numerical simulation results not only show the consistence with the theoretical analysis but also display complex dynamical behaviors, including period-n orbits, crisis, some chaotic attractors, period-doubling bifurcation to chaos, quasi-period behaviors to chaos, chaos to quasi-period behaviors, bubble and onset of chaos.展开更多
基金Supported by the National Natural Science Foundation of China(71303181)the Science Foundation of Ministry of Education of China(11YJC790004)+3 种基金China Postdoctoral Science Foundation Funded Project(2014M550864)the Fundamental Research Funds for the Central Universities of China(K50511060001)supported by China Scholarship Council(201406965014) while the first author was visiting George Mason UniversityResearch Funds for Research Base of Modern Service Industry in Hunan Province(16jdmszd01)
文摘The purpose of this paper is to investigate the macroeconomic effect of pollution emission in an overlapping generation system. This is done through constructing an endogenous economy which generates pollution and environment deterioration. It shows how different level of pollution emission could cause complexity such as fold bifurcation in this system. In addition, numerical simulations are provided to show the emergency of complexity.
文摘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.
基金Supported by the National Science Foundations of China(10671063 and 61571052)
文摘In this paper, Mira 2 map is investigated. The conditions of the existence for fold bifurcation, flip bifurcation and Naimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. And the conditions of the existence for chaos in the sense of Marroto are obtained. Numerical simulation results not only show the consistence with the theoretical analysis but also display complex dynamical behaviors, including period-n orbits, crisis, some chaotic attractors, period-doubling bifurcation to chaos, quasi-period behaviors to chaos, chaos to quasi-period behaviors, bubble and onset of chaos.
