Extracting information from dynamical data tends to be difficult when the underlying systems have nonlinearities. Although reconstruction of autonomous systems from data has been discussed frequently in the literature [1,4–7,10], little attention has been paid to the nonautonomous case. In this article, we discuss a method of drawing conclusions about the dynamical content of a driver that simu...

In this paper, transistor lasers (TLs) are used as an optical modulator for generation of ASK(Amplitude Shift Keying) and FSK (Frequency Shift Keying) optical signals. Our analysis is based on continuity equation, rate equations, and the theory of discontinuity of quasi-fermi level at the abrupt junction. Our simulation results indicate that, the specification of ASK and FSK optical signals, ar...

In this paper, we present a real time animator for dynamical systems that can be modeled as hybrid automata i.e. standard finite automata extended with differential equations. We describe its semantic foundation and its implementation in Java and C using CVODE, a software package for solving ordinary differential equations. We show how the animator is interfaced with the Uppaal tool to demonstr...

We present the effective action and self-consistency equations for the bosonic dynamical mean field approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations, we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the ...

In this article, we summarize some results on the existence and qualitative behavior of stochastic dynamical systems in infinite dimensions. The three main examples covered are stochastic systems with finite memory (stochastic functional differential equations-sfde’s), semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s). Due to limitations of...

We identify contact transformations which linearize the given equations in the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations to the same order. The identified contact transformations are not of Cole-Hopf type and are new to the literature. The linearization of Abel chain of equations is also demonstrated explicitly for the first time. The contact transf...

Cherednik attached to an affineHecke algebramodule a compatible systemof difference equations, called quantum affine Knizhnik–Zamolodchikov (KZ) equations. In the case of a principal series module, we construct a basis of power series solutions of the quantum affine KZ equations. Relating the bases for different asymptotic sectors gives rise to a Weyl group cocycle, which we compute explicitly ...

Dynamical systems described by equations of motion with the first-order time derivative (dissipative) terms of even and odd powers, and coefficients varying either in time or in space, are considered. Methods to obtain standard and nonstandard Lagrangians are presented and used to identify classes of equations of motion that admit a Lagrangian description. It is shown that there are two general...

This paper reviews the derivation of equations for slow dynamical processes in a variety of systems, including rotating rigid rotors, crystalline solids, isotropic and nematic elastomers, gels in an isotropic fluid background, and nematic liquid crystals. It presents a recent derivation of the Leslie–Ericksen equations for the dynamics of nematic liquid crystals that clarifies the nature of the...

In systems and control theory dynamical systems described by partial differential equations are known as distributed parameter systems. For modelling and dynamical analysis of distributed parameter systems wide possibilities are offered by virtual software environments as ANSYS, COMSOL Multiphysics, ProCAST, MODFLOW, based on numerical solution of sets of partial differential equations by finit...