In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes ...In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes in population density.In this paper,we consider a reaction-diffusion-advection model with nonlocal delay and Dirichlet boundary conditions.First of all,we investigate the well-posedness of solution of model.Then,the existence of positive steady state is proofed by implicit function theorem.Based on a priori estimate for the eigenvalue,we prove the stability of the positive steady state and conclude the associated distribution of Hopf bifurcation.Our research indicates that the combined effects of nonlocal and time delays have a certain impact on the dynamics of the model.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.展开更多
基金Supported by the Natural Science Foundation of Shanghai(23ZR1401700)National Natural Science Foundation of China(12471157)。
文摘In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes in population density.In this paper,we consider a reaction-diffusion-advection model with nonlocal delay and Dirichlet boundary conditions.First of all,we investigate the well-posedness of solution of model.Then,the existence of positive steady state is proofed by implicit function theorem.Based on a priori estimate for the eigenvalue,we prove the stability of the positive steady state and conclude the associated distribution of Hopf bifurcation.Our research indicates that the combined effects of nonlocal and time delays have a certain impact on the dynamics of the model.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
