Hopf bifurcation of integro-differential equations

Alexander Domoshnitsky; Yakov Goltser

Hopf bifurcation of integro-differential equations

מתמטיקה

פרסום מחקרי: פרסום בכתב עת › מאמר › ביקורת עמיתים

6 ציטוטים ‏(Scopus)

תקציר

A method reducing integro-differential equations (IDE's) to systems of ordinary differential equations is proposed. Stability and bifurcation phenomena in critical cases are studied using this method. An analog of Hopf bifurcation for scalar IDE's of first order is obtained. Conditions for existence of periodic solution are proposed. We conclude that phenomena typical for two dimensional systems of ODE's appear for scalar IDE's.

שפה מקורית	אנגלית
עמודים (מ-עד)	1-11
מספר עמודים	11
כתב עת	Electronic Journal of Qualitative Theory of Differential Equations
סטטוס פרסום	פורסם - 2000

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Link to publication in Scopus

פורמט ציטוט ביבליוגרפי

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title = "Hopf bifurcation of integro-differential equations",

abstract = "A method reducing integro-differential equations (IDE's) to systems of ordinary differential equations is proposed. Stability and bifurcation phenomena in critical cases are studied using this method. An analog of Hopf bifurcation for scalar IDE's of first order is obtained. Conditions for existence of periodic solution are proposed. We conclude that phenomena typical for two dimensional systems of ODE's appear for scalar IDE's.",

keywords = "Bifurcation, Integral equations, Periodic solution, Stability",

author = "Alexander Domoshnitsky and Yakov Goltser",

year = "2000",

language = "אנגלית",

pages = "1--11",

journal = "Electronic Journal of Qualitative Theory of Differential Equations",

issn = "1417-3875",

publisher = "University of Szeged",

}

TY - JOUR

T1 - Hopf bifurcation of integro-differential equations

AU - Domoshnitsky, Alexander

AU - Goltser, Yakov

PY - 2000

Y1 - 2000

N2 - A method reducing integro-differential equations (IDE's) to systems of ordinary differential equations is proposed. Stability and bifurcation phenomena in critical cases are studied using this method. An analog of Hopf bifurcation for scalar IDE's of first order is obtained. Conditions for existence of periodic solution are proposed. We conclude that phenomena typical for two dimensional systems of ODE's appear for scalar IDE's.

AB - A method reducing integro-differential equations (IDE's) to systems of ordinary differential equations is proposed. Stability and bifurcation phenomena in critical cases are studied using this method. An analog of Hopf bifurcation for scalar IDE's of first order is obtained. Conditions for existence of periodic solution are proposed. We conclude that phenomena typical for two dimensional systems of ODE's appear for scalar IDE's.

KW - Bifurcation

KW - Integral equations

KW - Periodic solution

KW - Stability

UR - https://www.scopus.com/pages/publications/3042584715

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AN - SCOPUS:3042584715

SN - 1417-3875

SP - 1

EP - 11

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

ER -

Hopf bifurcation of integro-differential equations

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