ChesterRep Collection:
http://hdl.handle.net/10034/6981
Wed, 28 Sep 2016 06:46:59 GMT2016-09-28T06:46:59ZNumerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh-Nagumo equation
http://hdl.handle.net/10034/619088
Title: Numerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh-Nagumo equation
Authors: Ford, Neville J.; Lima, Pedro M.; Lumb, Patricia M.
Abstract: In this work we introduce and analyse a stochastic functional equation, which contains both delayed and
advanced arguments. This equation results from adding a stochastic term to the discrete FitzHugh-Nagumo
equation which arises in mathematical models of nerve conduction. A numerical method is introduced
to compute approximate solutions and some numerical experiments are carried out to investigate their
dynamical behaviour and compare them with the solutions of the corresponding deterministic equation.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6190882016-01-01T00:00:00ZQuenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control
http://hdl.handle.net/10034/618944
Title: Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control
Authors: Kavallaris, Nikos I.
Abstract: In the current paper, we consider a stochastic parabolic equation which actually serves as a mathematical model describing the operation of an electrostatic actuated micro-electro-mechanical system (MEMS). We first present the derivation of the mathematical model. Then after establishing the local well-posedeness of the problem we investigate under which circumstances a {\it finite-time quenching} for this SPDE, corresponding to the mechanical phenomenon of {\it touching down}, occurs. For that purpose the Kaplan's eigenfunction method adapted in the context of SPDES is employed.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6189442016-01-01T00:00:00ZAddendum to the article: On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line
http://hdl.handle.net/10034/617231
Title: Addendum to the article: On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line
Authors: Antonopoulou, Dimitra; Kamvissis, Spyridon
Abstract: We present a short note on the extension of the results of [1] to the case of non-zero
initial data. More specifically, the defocusing cubic NLS equation is considered on the half-line
with decaying (in time) Dirichlet data and sufficiently smooth and decaying (in space) initial data.
We prove that for this case also, and for a large class of decaying Dirichlet data, the Neumann
data are sufficiently decaying so that the Fokas unified method for the solution of defocusing NLS is applicable.
Description: This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [forthcoming].Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6172312016-01-01T00:00:00ZStability analysis of a continuous model of mutualism with delay dynamics
http://hdl.handle.net/10034/609519
Title: Stability analysis of a continuous model of mutualism with delay dynamics
Authors: Roberts, Jason A.; Joharjee, Najwa G.
Abstract: In this paper we introduce delay dynamics to a coupled system of
ordinary differential equations which represent two interacting species
exhibiting facultative mutualistic behaviour. The delays are represen-
tative of the beneficial effects of the indirect, interspecies interactions
not being realised immediately. We show that the system with delay
possesses a continuous solution, which is unique. Furthermore we show
that, for suitably-behaved, positive initial functions that this unique
solution is bounded and remains positive, i.e. both of the components
representing the two species remain greater than zero. We show that
the system has a positive equilibrium point and prove that this point
is asymptotically stable for positive solutions and that this stability
property is not conditional upon the delays.Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10034/6095192016-05-01T00:00:00Z