具投放的中立型时滞竞争扩散系统正周期解的存在性

利用Nussbaum 度理论建立了具投放的中立型时滞竞争扩散系统 x′₁(t)=x₁(t)[a₁(t)-b₁(t)x₁(t)-c₁(t)y(t) ]+D₁(t)[x₂(t)-x₁(t)]+S₁(t), x′₂(t)=x₂(t)[a₂(t)-b₂(t)x₂(t)]+D₂(t)[x₁(t)-x₂(t) ]+S₂(t), y′(t)=y(t)[a₃(t)-b₃(t)y(t)-α(t)y(t-τ₁(t))-β(t) ∫⁰_τ k(s)y(t+s)ds -γ(t)y’(t-τ₂(t))-c₃(t)x₁(t)]. 存在正周期解的一个充分条件.     

The existence of periodic solutions of impulsive differential equations of mixed type

1　ＰｒｏｂｌｅｍｉｎｔｈｅＲｅｓｅａｒｃｈｏｆＴｏｒｏｉｄＩｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｉｓａｎｅｗｉｍｐｏｒｔａｎｔｂｒａｎｃｈｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ.Ｉｎ1989,[1],[2]ｓｙｓｔｅｍａｔｉｃａｌｌｙｓｕｍｍａｒｉｚｅｄｒｅｓｅａｒｃｈｗｏｒｋａｂｏｕｔｉｍｐｕｌｓｉｖｅｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｔｈｅｒｅａｒｅｍａｎｙｌｉｔｅｒａｔｕｒｅｓｄｅａｌｉｎｇｗｉｔｈｔｈｅｏｓｃｉｌｌａｔｉｏ…     

奇数阶中立型时滞微分方程的线性化振动性

考虑奇数阶中立型非线性微分方程ｄ＾ｎ／ｄｔ＾ｎ（ｘ（ｔ）－Ｐ（ｔ）ｇ（ｘ（ｔ－τ）））＋Ｑ（ｔ）ｈ（ｘ（ｔ－σ））＝０。本文在允许Ｐ（ｔ）－１振动的条件下给出了该方程的几个线性化振动结果。     

PERIODIC SOLUTIONS AND STABILITY ANALYSIS FOR NEURAL NETWORKS WITH TIME-VARYING DELAY

1 IntroductionIt is well known that both in biological and man-made neural systems, inte-gl.ation afld communication delays are ubiquitous, and often become sources ofinstabilitY' The de1ays in electronic neural networks are usually time varying,and sometimes vary vio1ently with time due to the finite switching speed ofamplifiers and faults in the electrical circuit. They s1ow down the transmissionrate and tend to introduce some degree of instability in circuits. Therefore,fast response must …