Active Magnetic Bearings (AMBs) have been widely used in industry, aeronautics and astronautics for some significant advantages. The sensor is one of the important parts of the electromagnetic bearing system, the features of the sensor can affect the performance of the whole system. The nonlinear electromagnetic force may cause the considerable oscillations of the rotor with some parametric exc...

This article analyzes a nonlinear system of first-order difference equations with periodic and non-periodic boundary conditions. Some sufficient conditions are presented under which: potential solutions to the equations will satisfy certain a priori bounds; and the equations will admit at least one solution. The methods involve new dynamic inequalities and use of Brouwer degree theory. The new ...

The computation of periodic orbits of nonlinear mappings or dynamical systems can be achieved by applying a root-finding method. To determine a periodic solution, an initial guess should be located within a proper area of the mapping or a surface of section of the phase space of the dynamical system. In the case of Newton or Newton-like methods these areas are the basins of convergence correspo...

In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: ′ 1 ( ) ( ) ( ( ), , ( )) ( ), n u t Au t F u t r u t r g t + = − ... − + where : ( ) A D A H H ⊂ → is a positive definite selfadjoint operator, : n F H H → α is a nonlinear mapping, 1 , , n r r ... are nonnegative constants, and ( ) ( ; ) g t C H ∈  is bounded. Motivated by [1] ...

The continuum limit of a recently-proposed model for charge transport in resonanttunneling semiconductor superlattices is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, supplemented by shock and entropy conditions. For appropriate parameter values, a time-periodic solution is found in numerical simulations of the model. An ...

Periodic progressive waves in shallow to transitional water are described by a Cnoidal Approximation wave theory. The formulation is analytical and largely classical. Periodic waves are assumed, so that the theory does not extend to solitary waves. The solution is completed numerically, as a problem in nonlinear optimisation. The suitability of the theory in shallow to transitional water is dem...

In this paper, we investigate the existence of nontrivial periodic solutions for an integrated pest management model which is impulsively controlled by means of biological and chemical controls used in a periodic fashion. For this model, a nonlinear incidence rate is employed to describe the transmission of the disease which is induced through the use of the biological control, while the chemic...

The delayed feedback control (DFC) is a control method for stabilizing unstable periodic orbits in nonlinear autonomous differential equations. We give an important relationship between the characteristic multipliers of the linear variational equation around an unstable periodic solution of the equation and those of its delayed feedback equation. The key of our proof is a result about the spect...