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In natural systems (such as those in natural world) and manmade systems (such as those in engineering applications), nonlinearity, one of the fundamental characteristics exhibited in simple and comp...
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems resu...
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation tha...
In this paper, by using normal form theory we give some criteria of nonexistence of formal first integrals for general nonlinear systems under resonance. As application, we also give a criterion for n...
We represent an algorithm reducing a big class of systems of (M + 1)-dimensional scalar nonlinear partial differential equations (PDEs) to the systems ofM-dimensional first order PDEs. Thus, we integr...
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and eq...
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scalin...
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scalin...
A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in dif...
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples $L_t=[H,L]-fL$ where L is a 2D Schrodinger Operator. This approach was invented by S.Manakov and B.Dubrovi...
The standard equations of linear elasticity have served well over many generations to describe small displacements of elastic systems subject to a variety of forces and/or stresses. However, computati...
Assuming that the behaviour of a nonlinear stochastic system can be described by a Markovian diffusion approximation and that the evolution equations can be reduced to a system of ordinary differentia...
An adaptive iterative learning control(ILC) approach is proposed for a class of uncertain nonlinear systems without prior knowledge about system control directions. The Nussbaum-type gain and the posi...

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