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Hopf bifurcation formula for first order differential-delay equations
Hopf bifurcation Differential delay equation DDE Retarded functional differential equation RFDE
2015/8/27
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The ...
Dynamics of a model of two delay-coupled relaxation oscillators
Coupled oscillators Devil’s Staircase Delay-differential equations
2015/8/27
This paper investigates the dynamics of a new model of two coupled relaxation oscilla-tors. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach wit...
Periodic motions in DDE (Differential-Delay Equations) are typically 4 created in Hopf bifurcations. In this chapter we examine this process from several 5 points of view. Firstly we use Lindstedt’s p...
Existence of S-asymptotically ω-periodic solutions for abstract fractionalintegro-differential equations with infinite delay
S-asymptotically ω-periodic mild solutions Fractional integral-differential equation Solution operator Fixed point theorems
2011/10/11
In this paper, existence of S-asymptotically ω-periodic mild solutions for abstract integro-differential equationwith fractional order is considered. The main results are obtained bythe contraction ma...
Nonlinear Stabilization under Sampled and Delayed Measurements, and with Inputs Subject to Delay and Zero-Order Hold
feedback stabilization time-delay systems sampled-data systems nonlinear control
2011/1/20
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the ...
Bohl-Perron type stability theorems for linear difference equations with infinite delay
Bounded delay uniform stability Perron’s property phase space
2010/12/15
Relation between two properties of linear difference equations with infinite delay is inves-
tigated: (i) exponential stability, (ii) ℓp-input ℓq-state stability (sometimes is called Perr...
Boolean delay equations on networks: An application to economic damage propagation
Boolean delay equations networks economic damage propagation
2010/4/27
We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for stu...
This paper deals with the relationship between asymptotic behavior
of the numerical solution and that of the true solution itself for
fixed step-sizes. The numerical solution is viewed as a dynamica...
This paper deals with the stability analysis of $\theta -$methods for the
numerical solution of delay differential equations (DDEs). We focus on
the behaviour of such methods in the solution of the ...
Asymptotic Behavior of Solutions to a Class of Systems of Delay Differential Equations
asymptotic behavior delay differential equation $\omega$-limit set
2007/12/10
The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a cons...
Oscillation of nonlinear neutral delay differential equations of second-order with positive and negative coefficients
Delay differential equations neutral nonlinear oscillation second-order
2010/2/25
Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-g))]''+p(t) g(x(t-a)) -q(t) g(x(t-b )) = s(t) where t\geq t0, g,a,b \in R+ with a \geq b, r ...
Oscillation of higher-order nonlinear delay differential equations with oscillatory coefficients
Neutral differential equations, positive and oscillating coefficients
2010/2/25
A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p...