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In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation ${(r (t) Φ (u^{'} (t)))}^{'} + c (t) Φ (u (t)) = 0,$ where (i) $r, c \in C ([t_{0}, \infty)$ , $ℝ : = (- \infty, \infty))$ and $r (t) > 0$ on $[t_{0}, \infty)$ for some $t_{0} \geq 0$ ; (ii) $Φ (u) = {| u |}^{p - 2} u$ for some fixed number $p > 1$ . We also generalize some results of Hille-Wintner, Leighton and Willet.

Some remarks on a recent third order nonlinear oscillation result

G. G. Hamedani (1985)

Časopis pro pěstování matematiky

Some results on the oscillatory and asymptotic behavior of the solutions of differential equations with deviating arguments

Christos G. Philos (1979)

Archivum Mathematicum

Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System

K. E. Gordon, I. M.M. van Leeuwen, S. Laín, M. A.J. Chaplain (2009)

Mathematical Modelling of Natural Phenomena

In this paper we investigate the role of spatial effects in determining the dynamics of a subclass of signalling pathways characterised by their ability to demonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of the p53 network that accounts for both a negative feedback and a transcriptional delay. We show that the formation of protein density patterns can depend on the shape of the cell, position of the nucleus, and the protein diffusion rates. The temporal...

Stability analysis of uncertain complex-variable delayed nonlinear systems via intermittent control with multiple switched periods

Song Zheng (2018)

Kybernetika

In this paper, an intermittent control approach with multiple switched periods is proposed for the robust exponential stabilization of uncertain complex-variable delayed nonlinear systems with parameters perturbation, in which the considered complex systems have bounded parametric uncertainties. Based on the Lyapunov stability theory and comparison theorem of differential equations, some stability criteria are established for a class of uncertain complex delayed nonlinear systems with parameters...

Stability implications on the asymptotic behavior of nonlinear systems.

Chiou, Kuo-Liang (1982)

International Journal of Mathematics and Mathematical Sciences

Stable closed orbits in plane autonomous dynamical systems.

Dieter Erle (1979)

Journal für die reine und angewandte Mathematik

Strong oscillations for second order nonlinear functional differential equations.

Yan, Jurang (1990)

International Journal of Mathematics and Mathematical Sciences

Synchronization in ensembles of coupled maps with a major element.

Omelchenko, Iryna, Maistrenko, Yuri, Mosekilde, Erik (2005)

Discrete Dynamics in Nature and Society

Synchronization of fractional-order chaotic systems with multiple delays by a new approach

Jianbing Hu, Hua Wei, Lingdong Zhao (2015)

Kybernetika

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

Jian Gen Wang, Jianping Cai, Mihua Ma, Jiuchao Feng (2008)

Kybernetika

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.

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