TY - JOUR
T1 - Convergence in lotka-volterra-type delay systems without instantaneous feedbacks
AU - Kuang, Yang
AU - Smith, Hal
N1 - Funding Information:
* Research supported by NSF Grant DMS 8922654.
PY - 1993
Y1 - 1993
N2 - Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-type system if some of the delays are small, and initial functions are small and smooth, then the convergence of its positive steady state follows that of the undelayed system or the corresponding system whose instantaneous negative feedback dominates. In particular, we establish explicit expressions for allowable delay lengths for such convergence to sustain.
AB - Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-type system if some of the delays are small, and initial functions are small and smooth, then the convergence of its positive steady state follows that of the undelayed system or the corresponding system whose instantaneous negative feedback dominates. In particular, we establish explicit expressions for allowable delay lengths for such convergence to sustain.
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U2 - 10.1017/S0308210500021235
DO - 10.1017/S0308210500021235
M3 - Article
AN - SCOPUS:0012193361
SN - 0308-2105
VL - 123
SP - 45
EP - 58
JO - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
IS - 1
ER -