In this paper, the joint state and fault estimation problem is investigated for a class of discrete-time complex networks with measurement saturations stochastic nonlinearities. The difference between actual saturated regarded as an unknown input system thus re-organized singular system. An appropriate estimator designed each node which aims to estimate states loss actuator effectiveness simult...

We study the existence and multiplicity of positive solutions for a system Riemann–Liouville fractional differential equations with sequential derivatives, parameters sign-changing singular nonlinearities, subject to nonlocal coupled boundary conditions which contain Riemann–Stieltjes integrals various derivatives. In proof our main results we use nonlinear alternative Leray–Schauder type Guo–K...

A nonlinear black box structure represented by an affine three-layered state-space neural network with exogenous inputs is considered for nonlinear systems identification. Global stability conditions are derived based on Lyapunov’s stability theory and on the contraction mapping theorem. The problem of structural complexity is also addressed by defining an upper bound for the number of hidden l...

This paper considers the famous Fermi-Pasta-Ulam chain with periodic boundary conditions and quartic nonlinearities. Due to special resonances and discrete symmetries, the Birkhoff normal form of this Hamiltonian system is completely integrable, as was shown in [16]. We study how the level sets of the integrals foliate the phase space. Our study reveals all the integrable structure in the low e...

We present nonnegativity-preserving finite element schemes for a general class of thin film equations in multiple space dimensions. The equations are fourth order degenerate parabolic, and may contain singular terms of second order which are to model van der Waals interactions. A subtle discretization of the arising nonlinearities allows us to prove discrete counterparts of the essential estima...

Abstract Singular exponential nonlinearities of the form $$e^{h(x)\epsilon ^{-1}}$$ e h ( x ) ϵ - 1 with $$\epsilon >0$$ >...