文章基本信息

标题：Modeling Nonlinear Dynamical Systems
本地全文：下载
作者：A. A. Akintunde ; S. O. N. Agwuegbo ; O. E. Asiribo 等
期刊名称：Annals. Computer Science Series
印刷版ISSN：1583-7165
电子版ISSN：2065-7471
出版年度：2015
卷号：13
期号：1
页码：30-38
出版社：Mirton Publishing House, Timisoara
摘要：The study of stochastic phenomena has increased dramatically and intensified research activity in this area has been stimulated by the need to take into account random effects in complicated dynamical systems. Dynamical systems are ubiquitous and are considered to be stochastic processes. In this study, a nonlinear dynamical system was modeled as a solution to an Ito stochastic differential equation dx(t)=f(x(t),t)dt+g(x(t),t)dW(t) where W(t) denotes a Wiener or Brownian motion process while f and g are deterministic functions. The Ito Stochastic Differential Equation was applied to characterize the important functional of the solution process in some intervals [0,t],X(t) which satisfies the integral equation, X(t)=X(0)+∫f(s,X(s))ds+∫g(s,X(s))dW(s). The solution of the integral equation is a Lagenvin equation which is an Ornstein-Uhlenbeck (O-U) process dXt=α(Θ-Xt)dt+σdWt. The O-U process which is a Gaussian process was related to the world of time series analysis. The model was applied to Nigerian monetary exchange rate and compared with the existing models of monetary exchange rate. R package and the Akaike Information Criteria (AIC) were used to provide the model of best fit for the Nigerian monetary exchange rate as an autoregressive moving average of order one which is given to be St=(0.4287St-1)+(0.2099et-1)+et. The results obtained revealed that the structural diffusion model approach gives a first-order autoregressive moving average process in continuous time with differentiation in continuous time corresponding to differencing in discrete time. The derived structural diffusion model has the least AIC value of 1482.61 as compared to the AIC value of 2198.86 from the existing diffusion and normal models
关键词：Dynamical systems; Stochastic Differential Equation; Diffusion model; Markov processes