Strong oscillations for second order nonlinear functional differential equations.
Synchronization in ensembles of coupled maps with a major element.
Synchronization of fractional-order chaotic systems with multiple delays by a new approach
In this paper, we propose a new approach of designing a controller and an update rule of unknown parameters for synchronizing fractional-order system with multiple delays and prove the correctness of the approach according to the fractional Lyapunov stable theorem. Based on the proposed approach, synchronizing fractional delayed chaotic system with and without unknown parameters is realized. Numerical simulations are carried out to confirm the effectiveness of the approach.
Synchronization with error bound of non-identical forced oscillators
Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.
The existence of periodic solutions of an autonomous second order non-linear differential equation
The invariant cone of slowly oscillating solutions to two delay differential equations.
The nonlinear limit-point/limit-circle problem for higher order equations
We describe the nonlinear limit-point/limit-circle problem for the -th order differential equation The results are then applied to higher order linear and nonlinear equations. A discussion of fourth order equations is included, and some directions for further research are indicated.
The nonlinearly damped oscillator
We study the large-time behaviour of the nonlinear oscillatorwhere and is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case with real, . We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.
The Nonlinearly Damped Oscillator
We study the large-time behaviour of the nonlinear oscillator where m, k>0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case with α real, A>0. We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.
The period of oscillations in non-linear systems
The property (A) for a certain class of the third order ODE
The Schauder-Tychonoff Fixed Point Theorem and Applications
Tunnels-entonnoirs-peignes. IIe partie.
Two-point oscillatory solutions to system with relay hysteresis and nonperiodic external disturbance
We study an -dimensional system of ordinary differential equations with a constant matrix, a relay-type nonlinearity, and an external disturbance in the right-hand side. We consider a nonideal relay characteristic. The external disturbance is described by the product of an exponential function and a sine function with an initial phase as a parameter. We assume the matrix of the linear part and the vector at the relay characteristic such that, by a nonsingular transformation, the system is reduced...
Zovšeobecnená Liénardova diferenciálna rovnica
Асимптотический анализ ВАХ перехода Джозефсона
Об одной обратной задаче для уравнения Хилла. Численные эксперименты
Ограниченные решения и периодические колебания дифференциальных систем