Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||13|
|Journal||JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS|
|Early online date||22 Aug 2016|
|Publication status||Published - Jun 2018|
|Publication type||A1 Journal article-refereed|
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.