Search results for "Nonlinear system"
showing 10 items of 1446 documents
Remarks on the economic interpretation of Hopf bifurcations
1999
Abstract The Hopf bifurcation theorem has become a frequently used tool in the study of nonlinear dynamical economic systems. In this paper, it is shown that phenomena like multiple limit cycles, hysteresis loops and catastrophic transitions may possibly accompany a Hopf bifurcation. The theoretical argument is illustrated in Foley's liquidity cost–business cycle model.
Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1
1998
In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoret…
A SUBCRITICAL BIFURCATION FOR A NONLINEAR REACTION–DIFFUSION SYSTEM
2010
In this paper the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms is investigated. Through a linear stability analysis we show that the cross-diffusion term allows the pattern formation. To predict the form and the amplitude of the pattern we perform a weakly nonlinear analysis. In the supercritical case the Stuart-Landau equation is found, which rules the evolution of the amplitude of the most unstable mode. With the increasing distance from the bifurcation value of the cross-diffusion parameter, the weakly nonlinear analysis fails and a Fourier–Galerkin approach is adopted. In the subcritical case the weakly nonlinear analysis must be pushed u…
The Nature of Dielectric Nonlinearity in the Region of Diffused Phase Transition in Layered Ferroelectric BaBi2Nb2O9
2008
By studying the dielectric properties of BaBi 2 Nb 2 O 9 ceramics, a representative of layered ferroelectrics, significant dispersion of ϵ* has been revealed at low- and infra-low frequences in the region of phase transition. Dispersion of ϵ* observed in “low-temperature” region (T T m where the basic contribution to ϵ* is provided by processes of the Maxwell-Wagner relaxation.
Low frequency nonlinearity in layered ferroelectrics BaBi<inf>2</inf>Nb<inf>2</inf>O<inf>9</inf> and SrBi<inf&…
2010
The dielectric nonlinearity in layered ferroelectric ceramics of BaBi 2 Nb 2 O 9 and SrBi 2 Ta 2 O 9 is studied by analysing polarisation loops and measuring dielectric permittivity as a function of frequency. In case of BaBi 2 Nb 2 O 9 the system has a broad phase transition manifesting essential features of a slow relaxation of polarisation; in case of SrBi 2 Ta 2 O 9 the processes contributing to polarisation switching are driven by rearrangement of the domain structure.
Parametric nonlinear singular Dirichlet problems
2019
Abstract We consider a nonlinear parametric Dirichlet problem driven by the p -Laplacian and a reaction which exhibits the competing effects of a singular term and of a resonant perturbation. Using variational methods together with suitable truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence on the parameter of the set of positive solutions.
Dynamical formation of Proca stars and quasistationary solitonic objects
2018
We perform fully non-linear numerical simulations within the spherically symmetric Einstein-(complex)Proca system. Starting with Proca field distributions that obey the Hamiltonian, momentum and Gaussian constraints, we show that the self-gravity of the system induces the formation of compact objects, which, for appropriate initial conditions, asymptotically approach stationary soliton-like solutions known as Proca stars. The excess energy of the system is dissipated by the mechanism of \textit{gravitational cooling} in analogy to what occurs in the dynamical formation of scalar boson stars. We investigate the dependence of this process on the phase difference between the real and imaginary…
Some nonlinear properties of ferroelectric smart materials
2001
Four types of nonlinear properties of ferroelectric smart materials have been considered: nonlinear dynamics of the paraelectric–ferroelectric interphase boundaries, nonlinear equilibrium excitations}domain walls, nonlinear response of the domain structure near the first-order phase transition}wetting of domain walls}andnonlinear effects causedby external high magnetic fields. The above mentioned nonlinearities have been studied in ðBa; SrÞTiO3ðBSTÞ and PbðZr; TiÞO3ðPZTÞ. # 2001 Elsevier Science B.V. All rights reserved.
Nonlinear Analysis of Phase-locked Loop-Based Circuits
2013
Main problems of simulation and mathematical modeling of high-frequency signals for analog Costas loop and for analog phase-locked loop (PLL) are considered. Two approachers which allow to solve these problems are considered. In the first approach, nonlinear models of classical PLL and classical Costas loop are considered. In the second approach, engineering solutions for this problems are described. Nonlinear differential equations are derived for both approaches.
Analytical methods for computation of phase-detector characteristics and PLL design
2011
An effective analytical methods for computation of phase detector characteristics are suggested. For high-frequency oscillators new classes of such characteristics are described. Approaches to a rigorous nonlinear analysis of PLL are discussed.