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, 2005
Research on delayed neural networks with variable self-inhibitions, interconnection weights, and inputs is an important issue. In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection ...
Wenlian Lu, Tianping Chen
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Research on delayed neural networks with variable self-inhibitions, interconnection weights, and inputs is an important issue. In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection ...
Wenlian Lu, Tianping Chen
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Periodic Solutions of Periodic Competitive and Cooperative Systems
SIAM Journal on Mathematical Analysis, 1986Many mathematical models in the biological sciences give rise to the system \(x_ i'=F_ i(x,t)\), \(1\leq i\leq n\), \(x=(x_ 1,x_ 2,...,x_ n)\). The system is said to be cooperative or competitive according as \(\partial F_ i/x_ j\geq\) or \(\leq 0(i\neq j)\).
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Periodic Solutions of Integrodifferential Equations
Journal of the London Mathematical Society, 1985The author is investigating the existence of periodic solutions to the integrodifferential equation of Volterra type \[ (1)\quad x'(t)=h(t,x(t))+\int^{t}_{-\infty}q(t,s,x(s))ds, \] under the basic assumptions that \(h: R\times R^ n\to R^ n\), and \(q: R\times R\times R^ n\to R^ n\) are both continuous, h is periodic in t with period T, and \(q(t+T,s+T ...
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The Bifurcation of T-periodic Solutions into nT-periodic Solutions and TORI
1977My lecture on bifurcation and stability of solutions which branch from forced T-periodic solutions is based on the recent work of G. IOOSS and myself [1] and on my forthcoming paper on factorization theorems [2]. In general, forced T-periodic solutions bifurcate into subharmonic solutions with a fixed period τ(τ=nT; n=1,2,3,4) independent of the ...
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Existence Theorems for Periodic Solutions and Almost Periodic Solutions
1975First of all, we shall state some fixed point theorems without proofs. The following theorem is due to Brouwer. For the proof, see [5].
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