In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-de...In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.展开更多
利用重合度理论中的延拓定理和Lyapunov泛函方法,获得了一类具有无穷时滞的中立型泛函微分方程(x(t))+cx(t-σ))′=A(t,x(t))x(t)+integral from n=-∞ to 0 f(t,s,x(t+s)ds+sum from i=1 to p fi(t,x(t-τi(t))))周期解的存在性和全局...利用重合度理论中的延拓定理和Lyapunov泛函方法,获得了一类具有无穷时滞的中立型泛函微分方程(x(t))+cx(t-σ))′=A(t,x(t))x(t)+integral from n=-∞ to 0 f(t,s,x(t+s)ds+sum from i=1 to p fi(t,x(t-τi(t))))周期解的存在性和全局吸引性的一些容易验证的充分条件,推广和改进了已有文献的相关结果。展开更多
考虑如下具有无穷时滞的微分系统:x′(t)=A(t,x(t))x(t)+(integral from -∞to 0)f(t,s,x(s+ t))ds+(sum from i=1 to p) fi(t,x(t-T_i(t)))的周期解.利用重合度理论和构造适当的Lyapunov泛函得到上述系统周期解存在性和全局吸引性的充...考虑如下具有无穷时滞的微分系统:x′(t)=A(t,x(t))x(t)+(integral from -∞to 0)f(t,s,x(s+ t))ds+(sum from i=1 to p) fi(t,x(t-T_i(t)))的周期解.利用重合度理论和构造适当的Lyapunov泛函得到上述系统周期解存在性和全局吸引性的充分条件,推广了已有的结论,得到了新的结果.展开更多
文摘In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.
文摘利用重合度理论中的延拓定理和Lyapunov泛函方法,获得了一类具有无穷时滞的中立型泛函微分方程(x(t))+cx(t-σ))′=A(t,x(t))x(t)+integral from n=-∞ to 0 f(t,s,x(t+s)ds+sum from i=1 to p fi(t,x(t-τi(t))))周期解的存在性和全局吸引性的一些容易验证的充分条件,推广和改进了已有文献的相关结果。
文摘考虑如下具有无穷时滞的微分系统:x′(t)=A(t,x(t))x(t)+(integral from -∞to 0)f(t,s,x(s+ t))ds+(sum from i=1 to p) fi(t,x(t-T_i(t)))的周期解.利用重合度理论和构造适当的Lyapunov泛函得到上述系统周期解存在性和全局吸引性的充分条件,推广了已有的结论,得到了新的结果.
