In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

We consider the problem of estimating parameters and unobserved trajectories in nonlinear ordinary differential equations (ODEs) from noisy and partially observed data. We focus on a class of statespace models defined from the integration of the differential equation in the evolution equation. Within a Bayesian framework, we derive a nonsequential estimation procedure that infers the parameters...

A novel approach is presented to implement continuous Hop eld neural networks, which are modelled by a system of ordinary di erential equations (ODEs). The simulation of a continuous network in a digital computer implies the discretization of the ODE, which is usually carried out by simply substituting the derivative by the di erence, without any further theoretical justi cation. Instead, the n...

A MACSYMA program is presented which determines whether a given single nonlinear ODE or PDE with real polynomial terms fulfills the necessary conditions for having the Painlevd property. The program listing is given, together with a synopsis of the algorithm, a model of the output of the 0 "S program, a list of tested exarples and instructions to use the package. AMS (MOS) Subject Classificatio...

Fractional-order financial system introduced by W.-C. Chen 2008 displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreove...

Abstract: In this paper we investigate the complete integrability of the system of six coupled nonlinear ODEs, which arises in the ODE reduction of rotating stratified Boussinesq equations. We use Painlevé test to investigate the complete integrability of the system. And we conclude that the system is completely integrable only if the Rayleigh number Ra = 0. The singular solution of the system ...

This paper describes parallel histogram modification techniques with embedded morphological preprocessing methods within the CNN-UM framework. The procedure is formulated in terms of nonlinear partial differential equations (PDE) and approximated through finite differences in space, resulting in coupled nonlinear ordinary differential equations (ODE). The I/O mapping of the system (containing b...

Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed out through diagrams or maps of computed asymptotic solutions in a suitable parametric space. Applying this methodology to a nonlinear test equation, we compar...

The paper deals with polyhedral estimates for reachable tubes of differential systems with a multiplicative uncertainty, namely linear systems with set-valued uncertainties in initial states, additive inputs and coefficients of the system. We present nonlinear parametrized systems of ordinary differential equations (ODE) which describe the evolution of the parallelotope-valued estimates for rea...

Previously a complete ordinary differential equation (ODE) system was developed for tracking the solution x(~) of a parameterized system of nonlinear equations 0 = ~'(x,~) over an ~-interval [~0, ~]. This paper develops a two-phase complex homotopy continuation method for obtaining the required initial conditions at ~t °. An initial "short" artificial continuation is followed by a continuation ...