In this paper,we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrodinger equation on flat torus,which is based on BNF technique,the tame property and the analysis of the spec...In this paper,we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrodinger equation on flat torus,which is based on BNF technique,the tame property and the analysis of the spectrum of(-Δ)^(s).展开更多
In this paper,we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation(product)in a particular region.The model exhibits two equilibria,namely,the adopter-free an...In this paper,we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation(product)in a particular region.The model exhibits two equilibria,namely,the adopter-free and an interior equilibrium.The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number(BIN)R_(A).It is investigated that the adopter free steady-state is stable if R_(A)<1.By consideringτ(the adoption experience of the adopters)as the bifurcation parameter,we have been able to obtain the critical value ofτresponsible for the periodic solutions due to Hopf bifurcation.The direction and stability analysis of bifurcating periodic solutions has been performed by using the arguments of normal form theory and the center manifold theorem.Exhaustive numerical simulations in the support of analytical results have been presented.展开更多
In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of ext...In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.展开更多
A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multip...A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.展开更多
基金Supported by the National Natural Science Foundation of China(12101542,12371189,12371241).
文摘In this paper,we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrodinger equation on flat torus,which is based on BNF technique,the tame property and the analysis of the spectrum of(-Δ)^(s).
文摘In this paper,we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation(product)in a particular region.The model exhibits two equilibria,namely,the adopter-free and an interior equilibrium.The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number(BIN)R_(A).It is investigated that the adopter free steady-state is stable if R_(A)<1.By consideringτ(the adoption experience of the adopters)as the bifurcation parameter,we have been able to obtain the critical value ofτresponsible for the periodic solutions due to Hopf bifurcation.The direction and stability analysis of bifurcating periodic solutions has been performed by using the arguments of normal form theory and the center manifold theorem.Exhaustive numerical simulations in the support of analytical results have been presented.
基金the Support Provided by the I.K.G. Punjab Technical University,Kapurthala,Punjab,India,where one of us(RK) is a Research Scholar
文摘In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.
文摘A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.
