We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular ma...We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.展开更多
This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be qua...This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.展开更多
基金supported by the National Natural Science Foundation of China(1237119112071175)+4 种基金supported by the NSFC(1207117511901080)supported by the NSFC(12071175)the Fundamental Research Funds For the Central Universities(2412023YQ003)the Natural Science Foundation of Jilin Province(20200201253JC)。
文摘We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.
基金supported by National Basic Research Program of China (Grant No. 2013CB834100)National Natural Science Foundation of China (Grant Nos. 11571065,11171132 and 11201173)
文摘This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.
