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ON STABILITY AND BIFURCATION OF PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS
EL-SHEIKH, M. M. A.,EL-MAHROUF, S. A. A. 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1
The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.
On stability and bifurcation of periodic solutions of delay differential equations
M. M. A. El-Sheikh,S. A. A. El-Mahrouf 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2
The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.