ON THE INFLUENCE OF THE RESONANT FREQUENCIES RATIO ON A STABLE PERIODIC SOLUTION OF TWO IMPACTING OSCILLATORS

2006 ◽  
Vol 16 (12) ◽  
pp. 3707-3715 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Periodic Motion ◽  
Stable Periodic Solution ◽  
Resonant Frequencies ◽  
Stable Periodic

A system that consists of two impacting oscillators with damping has been considered in this paper. The goal of the studies was to determine the relation between the values of resonant frequencies of the oscillators and the existence of their stable periodic motion. This paper indicates various origins of the periodicity of motion and offers a some advice to the designers of systems with impacts. Especially, the results of the considerations point out some potentially dangerous consequences of the improper value of the resonant frequencies ratio.

ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF TWO IMPACTING OSCILLATORS WITH DAMPING

2004 ◽  
Vol 14 (11) ◽  
pp. 3931-3947 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Periodic Motion ◽  
Equations Of Motion ◽  
Analytical Determination ◽  
Stable Periodic Solution ◽  
Numerical Investigations ◽  
Stable Periodic ◽  
Existence Of Periodic Solutions ◽  
The Stability

A system that consists of two impacting oscillators with damping has been considered in this paper. In the first part, a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions are presented. The results of the computations carried out by these methods have been illustrated with a few examples. In the second part of the paper, the results of some numerical investigations are presented. The goal of these studies is to determine, in which regions of parameters characterizing the system, the periodic motion with one impact per period exists and is stable.

scholarly journals Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Weibing Wang ◽  
Jianhua Shen ◽  
Juan J. Nieto
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Effect ◽  
Two Dimensional ◽  
Stable Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Stable Periodic ◽  
Holling Type Functional Response

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

scholarly journals Global asymptotic stability in a periodic Lotka-Volterra system

1985 ◽  
Vol 27 (1) ◽  
pp. 66-72 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable ◽  
Stable Periodic

AbstractA set of easily verifiable sufficient conditions are obtained for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients.

scholarly journals Periodic Solutions of a System of Delay Differential Equations for a Small Delay

2002 ◽  
Vol 7 (2) ◽  
pp. 295
Author(s):  
Adu A.M. Wasike ◽  
Wandera Ogana
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Original System ◽  
System Of Equations ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Stable Periodic ◽  
Delay Differential

We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system.  This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem.   

scholarly journals Chemical reaction dynamics: analysis of the brusselator model

2010 ◽  
Vol 51 ◽  
Author(s):  
Liana Stonkienė ◽  
Donatas Švitra
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Nonlinear Differential Equations ◽  
Reaction Dynamics ◽  
Dynamics Analysis ◽  
Stable Periodic Solution ◽  
Brusselator Model ◽  
Chemical Reaction Dynamics ◽  
Stable Periodic

It is observed the differential equations system. The stable periodic solution of the nonlinear differential equations system is constructed, which is based on the theory of bifurcations.

scholarly journals Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Liya Yang ◽  
Xiangdong Xie ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Cooperative Effect ◽  
Stable Periodic Solution ◽  
Predator Species ◽  
Predator Prey ◽  
Stable Periodic ◽  
Extinction Property ◽  
Globally Stable

A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results.

scholarly journals Linear and nonlinear stability in nuclear reactors with delayed effects

2013 ◽  
Vol 18 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kostas Bučys ◽  
Donatas Švitra ◽  
Ramunė Vilkytė
Keyword(s):  
Periodic Solution ◽  
Nonlinear Analysis ◽  
Nuclear Reactor ◽  
Stable Solution ◽  
Stable Periodic Solution ◽  
Reactor Model ◽  
Delayed Effects ◽  
Stability Model ◽  
Stable Periodic ◽  
Asymptotically Stable Solution

The research of a nuclear reactor model has been observed, where the system consists of two differential equations with one delay. A linear analysis has been performed, the asymptotic stability model of the area D0 and D2 has been defined, in which a stable periodic solution of one frequency appears. In the nonlinear analysis the analytical expression of the solution is presented with the help of bifurcation theories. In the numerical experiment using the scientific simulation program “Model Maker” numerical Runge–Kutta IV series method asymptotically stable solution and a stable periodic solution has been received and compared to the stable periodic solution received in nonlinear analysis with the help of bifurcation theories.

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