DYNAMIC PROPERTIES OF A SYMMETRICALLY CONSERVATIVE TWO-MASS SYSTEM

2013 ◽  
Vol 23 (03) ◽  
pp. 1350039
Author(s):  
CHUNRUI ZHANG ◽  
BAODONG ZHENG
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Numerical Simulations ◽  
Dynamic Properties ◽  
Spatiotemporal Patterns ◽  
Hopf Bifurcations ◽  
Mass System ◽  
Numerical Examples ◽  
Functional Differential ◽  
Bifurcating Periodic Solution

A symmetrically conservative two-mass system with delay is considered. Using the symmetric functional differential equation theories, multiple Hopf bifurcations of the equilibrium at the origin are demonstrated. The existence of multiple branches of bifurcating periodic solution and their spatiotemporal patterns are obtained. Some numerical examples and the corresponding numerical simulations are used to illustrate the effectiveness of the obtained results.

On the existence of periodic solutions for autonomous retarded functional differential equations on R2

1986 ◽  
Vol 102 (3-4) ◽  
pp. 259-262 ◽  
Author(s):  
J. G. Dos Reis ◽  
R. L. S. Baroni
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Retarded Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

scholarly journals On periodic solutions to autonomous retarded functional differential equations

1990 ◽  
Vol 41 (3) ◽  
pp. 347-354
Author(s):  
Zhanyuan Hou
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Retarded Functional Differential Equations ◽  
Retarded Functional Differential Equation ◽  
Functional Differential ◽  
Necessary And Sufficient

Under the assumption that Ca = C([−r, 0], Sn−1(a)) is positively invariant for a > 0, two necessary and sufficient conditions are obtained for an autonomous retarded functional differential equation to have a non-trivial periodic solution in Ca. Moreover, a feasible sufficient condition is given, which is better for n = 2 than that given by Dos Reis and Baroni.

scholarly journals Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Positive Periodic Solution ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Mawhin’S Continuation Theorem ◽  
Volterra Models ◽  
Functional Differential ◽  
New Criteria

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory fork-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse:x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))],  t≠tk,  k∈Z+;  x(tk+)=x(tk-)+θk(x(tk)),  k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

scholarly journals On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lili Gao ◽  
Litan Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Brownian Motion ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we consider the random periodic solution to a neutral stochastic functional differential equation driven by Brownian motion. We obtain the existence and uniqueness of the random periodic solution by Banach fixed point theorem. Moreover, we introduce two examples to illustrate our results.

scholarly journals Heun Method Using to Solve System of NonLinear Functional Differential Equations

2007 ◽  
Vol 4 (4) ◽  
pp. 666-669
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Nonlinear Functional ◽  
Numerical Examples ◽  
Nonlinear Functional Differential Equation ◽  
First Order ◽  
Functional Differential

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

scholarly journals A note on periodic solutions of functional differential equations

1985 ◽  
Vol 8 (2) ◽  
pp. 413-415
Author(s):  
S. H. Chang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Functional Differential

The existence of periodic solution for a certain functional differential equation with quasibounded nonlinearity is established.

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