scholarly journals Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xinli Zhang ◽  
Shanliang Zhu
Keyword(s):  
Dynamic System ◽  
Time Scale ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic System ◽  
Two Dimensional ◽  
Differential Systems ◽  
Difference Systems ◽  
All Solutions ◽  
Forced Term

We consider a class of two-dimensional nonlinear dynamic system with a forced term on a time scale𝕋and obtain sufficient conditions for all solutions of the system to be oscillatory. Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also improve the oscillation results that have been established by Saker, 2005, since our results are not restricted to the case whereb(t)≠0for allt∈𝕋andg(u)=u. Some examples are given to illustrate the results.

scholarly journals On the oscillation of a nonlinear two-dimensional difference systems

2001 ◽  
Vol 32 (3) ◽  
pp. 201-209 ◽  
Author(s):  
E. Thandapani ◽  
B. Ponnammal
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Real Sequence ◽  
Two Dimensional ◽  
Difference System ◽  
Nonoscillatory Solutions ◽  
Difference Systems ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Strongly Sublinear

The authors consider the two-dimensional difference system$$ \Delta x_n = b_n g (y_n) $$ $$ \Delta y_n = -f(n, x_{n+1}) $$where $ n \in N(n_0) = \{ n_0, n_0+1, \ldots \} $, $ n_0 $ a nonnegative integer; $ \{ b_n \} $ is a real sequence, $ f: N(n_0) \times {\rm R} \to {\rm R} $ is continuous with $ u f(n,u) > 0 $ for all $ u \ne 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

scholarly journals Periodic solutions for dynamic equations on time scales

2009 ◽  
Vol 40 (2) ◽  
pp. 173-191
Author(s):  
Shun-Tang Wu ◽  
Long-Yi Tsai
Keyword(s):  
Dynamic System ◽  
Periodic Solutions ◽  
Time Scales ◽  
Nonlinear Dynamic ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic System ◽  
Dynamic Equations ◽  
Inequality Techniques ◽  
Existence Of Periodic Solutions

The second order nonlinear dynamic system on time scales is considered. Some sufficient conditions for the existence of periodic solutions are given. Differential inequality techniques and the method of mixed monotony are used.

scholarly journals On quasiperiodic oscillations of a nonlinear dynamic system of Liapunov type with time lag

1998 ◽  
Vol 20 (1) ◽  
pp. 1-8
Author(s):  
Le Xuan Can
Keyword(s):  
Power Series ◽  
Dynamic System ◽  
Nonlinear Dynamic ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic System ◽  
Quasiperiodic Solution ◽  
Necessary And Sufficient ◽  
Quasiperiodic Oscillations ◽  
Oscillating Processes

The paper is concerned with the investigation of the quasiperiodic oscillations of a nonlinear dynamic system of Liapunov type with time lag. The following results are obtained:- The necessary and sufficient conditions for the existence of the quasiperiodic solution describing the oscillating processes.- The approximate quasiperiodic solution in the power series.- The quasiperiodic oscillations of a nonlinear dynamic system of Duffing type with the quasiperiodic perturbations.

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