scholarly journals The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Han Xu ◽  
Yinlai Jin
Keyword(s):  
Functional Analysis ◽  
Asymptotic Expansion ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Smooth Solution ◽  
Time Delays ◽  
Boundary Function ◽  
Interior Layer ◽  
Differential Systems ◽  
Delay Differential

We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer att=σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.

scholarly journals Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Guodong Liu ◽  
Xiaohong Wang ◽  
Xinzhu Meng ◽  
Shujing Gao
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Persistence In Mean ◽  
Predator Prey Model ◽  
Prey System ◽  
Delay Differential ◽  
Lévy Jumps

In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

Estimation of Time-Delays Using the Characteristic Roots of Delay Differential Equations

2011 ◽  
Author(s):  
Sun Yi ◽  
Sangseok Yu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Delay Systems ◽  
Lambert W Function ◽  
Short Paper ◽  
Characteristic Roots ◽  
General Systems ◽  
Delay Differential ◽  
Estimation Of Time

In this short paper, the preliminary result of a new method for estimation of time-delays of time-delay systems is presented. The presented method makes use of the Lambert W function, and is for scalar first-order delay differential equations (DDEs). Possible extension to general systems of DDEs and application to physical systems are also discussed.

scholarly journals Tumour Oscillation Analysis in Angiogenesis Models

2006 ◽  
Vol 1 ◽  
pp. 330
Author(s):  
P. Daugulis
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Oscillation Analysis ◽  
Point Analysis ◽  
Delay Differential

In this paper we describe Hopf point analysis for several systems of ordinary and time delay differential equations which encode the most important assumptions concerning anguigenesis processes induced by tumours It is shown that in most cases Hopf points exist only if time delays are nonzero and for most nonzero time delays there are Hopf points in these families of models.

EXISTENCE AND BIFURCATION OF PERIODIC SOLUTIONS OF THREE-DIMENSIONAL DELAY DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 14 (11) ◽  
pp. 3921-3929 ◽  
Author(s):  
PING BI ◽  
MAOAN HAN
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Three Dimensional ◽  
Hopf Bifurcations ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
Delay Differential

In this paper, we develop Kaplan–Yorke's method and consider the existence of 2r/(2k+1)-periodic solutions for certain three-dimensional delay differential systems. We also study Hopf bifurcations of this kind of periodic solutions for the system with a parameter and present some application examples of our main results.

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