Abstract: Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.
Abstract: In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.
Abstract: This paper considers the development of a two-point
predictor-corrector block method for solving delay differential
equations. The formulae are represented in divided difference form
and the algorithm is implemented in variable stepsize variable order
technique. The block method produces two new values at a single
integration step. Numerical results are compared with existing
methods and it is evident that the block method performs very well.
Stability regions of the block method are also investigated.
Abstract: In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.
Abstract: In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.