We study the oscillatory behavior, the periodicity and the asymptotic behavior of the positive solutions of the system of two nonlinear difference equations xn+1 = A+ xn−1/yn and yn+1 =A+yn−1/xn, where A is a positive constant, and n= 0,1, . . . .

The probability distribution of a Markov chain is viewed as the information state of an additive optimization problem. This optimization problem is then generalized to a product form whose information state gives rise to a generalized notion of probability distribution for Markov chains. The evolution and the asymptotic behavior of this generalized or “risk-sensitive” probability distribution i...

This paper develops a two-scale asymptotic homogenization method for periodic composite Kirchhoff plates. In this method, three-dimensional (3D) plate problem is simplified as problem, which governed by fourth-order uniformly elliptic partial differential equation (PDE) with periodically oscillating coefficients. Then, solution in an expansion form presented the PDE, and it found that first-ord...

Abstract We report the occurrence of bursting oscillations in a gyroscope oscillator driven by low-frequency external period forcing. The patterns arise when either frequency or amplitude excitation force is varied. They take form pulse-shaped explosions (PSEs) wherein periodic attractors lower periodicity disappear due to loss asymptotic stability equilibrium point between resting and active s...

In this paper, we investigate the stability and periodicity of a class state-dependent switched systems with all unstable subsystems by means energy analysis. We firstly transform reversibly into form second order mechanical systems, then construct functions calculating sum kinetic potential energies each subsystem. After that, two switching lines, derived from lines largest smallest drops, mak...

Abstract. In this paper, we derive and analyze a Reissner–Mindlin–like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger– Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymp...

The frequency-domain problem of water-wave propagation through a periodically arranged infinite array of structures is solved using the method of matched asymptotic expansions for both shallow and deep water; the structures are assumed to be small relative to the wave length and the array periodicity, and may be fixed or float freely. Explicit approximations to the frequencies of propagating mo...