We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under assumption that preserve equilibrium state limit system, oscillate with asymptotically constant frequency, and satisfy nonresonance condition. discuss long-term behavior perturbed trajectories neighborhood state. describe conditions perturbation parameters guarantee preservation or loss stability...

The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization “domain wall width” was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energ...

The bidimensional Duffing oscillator (2DHD) is a parametric Hamiltonian system, integrable by elliptic functions, which includes as particular cases the isotropic oscillator and the classic Hamiltonian Duffing model. The Stark effect, after the KS transformation is used and the parameters are properly chosen, may be studied as a couple of 2DHD. A particular case of 2DHD system has been consider...

A method for the development of mathematical models for dynamic systems with arbitrary nonlinearides from measured data is described. The method involves the use of neural networks as embedded processors indynamic system simuation models. The technique is demonstrated through generation of models for anharmonic oscillators described by the Duffing Equation and the Van der Pol Equation from meas...

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...