메뉴 건너뛰기




Volumn 4, Issue 2, 2009, Pages 1-27

Approximating the stability region for a differential equation with a distributed delay

Author keywords

delay differential equations; delay independent stability; distributed delay; linear stability

Indexed keywords

BIOLOGICAL MODELS; DELAY DIFFERENTIAL EQUATIONS; DELAY INDEPENDENT; DISCRETE DELAY; DISTRIBUTED DELAY; DISTRIBUTED DELAYS; EQUILIBRIUM POINT; EXACT DISTRIBUTION; GAMMA DISTRIBUTION; INDEPENDENT STABILITY; LINEAR STABILITY; MINIMAL INFORMATION; MOMENTS OF THE DISTRIBUTION; STABILITY REGIONS;

EID: 77951135044     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20094201     Document Type: Article
Times cited : (54)

References (33)
  • 1
    • 24344475745 scopus 로고    scopus 로고
    • A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia
    • DOI 10.1137/040604698
    • M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math., 65 (2005), 1328-1352. (Pubitemid 41343748)
    • (2005) SIAM Journal on Applied Mathematics , vol.65 , Issue.4 , pp. 1328-1352
    • Adimy, M.1    Crauste, F.2    Ruan, S.3
  • 2
    • 15844377066 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics
    • DOI 10.1016/j.nonrwa.2004.12.010, PII S1468121804001208, Modelling, Analysis, and Theory of Dynamic Populations
    • M. Adimy, F. Crauste, S. Ruan. Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonl. Anal.: Real World Appl., 6 (2005), 651-670. (Pubitemid 40420740)
    • (2005) Nonlinear Analysis: Real World Applications , vol.6 , Issue.4 , pp. 651-670
    • Adimy, M.1    Crauste, F.2    Ruan, S.3
  • 3
    • 77952669436 scopus 로고    scopus 로고
    • Time delays in epidemic models: Modeling and numerical considerations
    • chapter 13, Springer, Dordrecht
    • J. Arino, P. van den Driessche. Time delays in epidemic models: modeling and numerical considerations, in Delay differential equations and applications, chapter 13, 539-558. Springer, Dordrecht, 2006.
    • (2006) Delay Differential Equations and Applications , pp. 539-558
    • Arino, J.1    Van Den Driessche, P.2
  • 4
    • 9744234606 scopus 로고    scopus 로고
    • Distributed delays facilitate amplitude death of coupled oscillators
    • F.M. Atay. Distributed delays facilitate amplitude death of coupled oscillators. Phys. Rev. Lett., 91 (2003), 094101.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 094101
    • Atay, F.M.1
  • 5
    • 30344466094 scopus 로고    scopus 로고
    • Oscillator death in coupled functional differential equations near Hopf bifurcation
    • DOI 10.1016/j.jde.2005.01.007, PII S0022039605000331
    • F.M. Atay. Oscillator death in coupled functional differential equations near Hopf bifurcation. J. Diff. Eqs., 221 (2006), 190-209. (Pubitemid 43056755)
    • (2006) Journal of Differential Equations , vol.221 , Issue.1 , pp. 190-209
    • Atay, F.M.1
  • 6
    • 70349976355 scopus 로고    scopus 로고
    • Delayed feedback control near Hopf bifurcation
    • F.M. Atay. Delayed feedback control near Hopf bifurcation. DCDS, 1 (2008), 197-205.
    • (2008) DCDS , vol.1 , pp. 197-205
    • Atay, F.M.1
  • 10
    • 0036754107 scopus 로고    scopus 로고
    • Global stability of neural networks with distributed delays
    • DOI 10.1016/S0893-6080(02)00039-4, PII S0893608002000394
    • Y. Chen. Global stability of neural networks with distributed delays. Neur. Net., 15 (2002), 867-871. (Pubitemid 35303333)
    • (2002) Neural Networks , vol.15 , Issue.7 , pp. 867-871
    • Chen, Y.1
  • 11
    • 33846426308 scopus 로고    scopus 로고
    • Global asymptotic stability of delayed Cohen-Grossberg neural networks
    • DOI 10.1109/TCSI.2005.856047
    • Y. Chen. Global stability of delayed Cohen-Grossberg neural networks. IEEE Trans. Circuits Syst.-I, 53 (2006), 351-357. (Pubitemid 46395411)
    • (2006) IEEE Transactions on Circuits and Systems I: Regular Papers , vol.53 , Issue.2 , pp. 351-357
    • Chen, Y.1
  • 13
    • 0000209631 scopus 로고
    • Discrete delay, distributed delay and stability switches
    • K.L. Cooke, Z. Grossman. Discrete delay, distributed delay and stability switches. J. Math. Anal. Appl., 86 (1982), 592-627.
    • (1982) J. Math. Anal. Appl. , vol.86 , pp. 592-627
    • Cooke, K.L.1    Grossman, Z.2
  • 14
    • 0003196710 scopus 로고
    • Integrodifferential equations and delay models in population dynamics
    • Springer-Verlag, Berlin, New York
    • J.M. Cushing. Integrodifferential equations and delay models in population dynamics, Vol. 20 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin, New York, 1977.
    • (1977) Lecture Notes in Biomathematics , vol.20
    • Cushing, J.M.1
  • 15
    • 38549148451 scopus 로고    scopus 로고
    • Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
    • T. Faria, J.J. Oliveira. Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. J. Diff. Eqs., 244 (2008), 1049-1079.
    • (2008) J. Diff. Eqs. , vol.244 , pp. 1049-1079
    • Faria, T.1    Oliveira, J.J.2
  • 17
    • 0001075269 scopus 로고
    • Stability in asymmetric Hopfield nets with transmission delays
    • K. Gopalsamy and X.-Z. He. Stability in asymmetric Hopfield nets with transmission delays. Physica D, 76 (1994), 344-358.
    • (1994) Physica D , vol.76 , pp. 344-358
    • Gopalsamy, K.1    He, X.-Z.2
  • 19
    • 33645084765 scopus 로고
    • Circular cause systems in ecology
    • G.E. Hutchinson. Circular cause systems in ecology. Ann. N.Y. Acad. Sci., 50 (1948), 221-246.
    • (1948) Ann. N.Y. Acad. Sci. , vol.50 , pp. 221-246
    • Hutchinson, G.E.1
  • 20
    • 19444371087 scopus 로고    scopus 로고
    • Will a large complex system with delays be stable?
    • V.K. Jirsa, M. Ding. Will a large complex system with delays be stable?. Phys. Rev. Lett., 93 (2004), 070602.
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 070602
    • Jirsa, V.K.1    Ding, M.2
  • 22
    • 0003302813 scopus 로고
    • Delay differential equations: With applications in population dynamics
    • Academic Press, New York
    • Y. Kuang. Delay differential equations: with applications in population dynamics, Vol. 191 of Mathematics in Science and Engineering. Academic Press, New York, 1993.
    • (1993) Mathematics in Science and Engineering , vol.191
    • Kuang, Y.1
  • 23
    • 0035254276 scopus 로고    scopus 로고
    • Bifurcation analysis on a two-neuron system with distributed delays
    • DOI 10.1016/S0167-2789(00)00197-4
    • X. Liao, K.-W. Wong, Z. Wu. Bifurcation analysis on a two-neuron system with distributed delays. Physica D, 149 (2001), 123-141. (Pubitemid 32086768)
    • (2001) Physica D: Nonlinear Phenomena , vol.149 , Issue.1-2 , pp. 123-141
    • Liao, X.1    Wong, K.-W.2    Wu, Z.3
  • 24
    • 0003289006 scopus 로고
    • Time lags in biological models
    • Springer-Verlag, Berlin; New York
    • N. MacDonald. Time lags in biological models, Vol. 27 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin; New York, 1978.
    • (1978) Lecture Notes in Biomathematics , vol.27
    • MacDonald, N.1
  • 26
    • 0021140794 scopus 로고
    • The dynamics of recurrent inhibition
    • M.C. Mackey, U. an der Heiden. The dynamics of recurrent inhibition. J. Math. Biol., 19 (1984), 211-225.
    • (1984) J. Math. Biol. , vol.19 , pp. 211-225
    • MacKey, M.C.1    Van Der Heiden, U.2
  • 28
    • 34248517099 scopus 로고    scopus 로고
    • Delay differential equations for single species dynamics
    • chapter 11, Springer, Dordrecht
    • S. Ruan. Delay differential equations for single species dynamics, in Delay differential equations and applications, chapter 11, 477-515. Springer, Dordrecht, 2006.
    • (2006) Delay Differential Equations and Applications , pp. 477-515
    • Ruan, S.1
  • 29
    • 1842635257 scopus 로고    scopus 로고
    • Dynamics of a two-neuron system with discrete and distributed delays
    • S. Ruan, R.S. Filfil. Dynamics of a two-neuron system with discrete and distributed delays. Physica D, 191 (2004), 323-342.
    • (2004) Physica D , vol.191 , pp. 323-342
    • Ruan, S.1    Filfil, R.S.2
  • 30
    • 2142762704 scopus 로고    scopus 로고
    • Complex dynamics is abolished in delayed recurrent systems with distributed feedback times
    • A. Thiel, H. Schwegler, C.W. Eurich. Complex dynamics is abolished in delayed recurrent systems with distributed feedback times. Complexity, 8 (2003), 102-108.
    • (2003) Complexity , vol.8 , pp. 102-108
    • Thiel, A.1    Schwegler, H.2    Eurich, C.W.3
  • 31
    • 0031258276 scopus 로고    scopus 로고
    • Competition in the chemostat: A distributed delay model and its global asymptotic behavior
    • PII S0036139995289842
    • G.S.K.Wolkowicz, H. Xia, S. Ruan. Competition in the chemostat: A distributed delay model and its global asymptotic behaviour. SIAM J. Appl. Math., 57 (1997), 1281-1310. (Pubitemid 127631484)
    • (1997) SIAM Journal on Applied Mathematics , vol.57 , Issue.5 , pp. 1281-1310
    • Wolkowicz, G.S.K.1    Xia, H.2    Ruan, S.3
  • 32
    • 0011689727 scopus 로고    scopus 로고
    • Global dynamics of a chemostat competition model with distributed delay
    • G.S.K. Wolkowicz, H. Xia, J. Wu. Global dynamics of a chemostat competition model with distributed delay. J. Math. Biol., 38 (1999), 285-316.
    • (1999) J. Math. Biol. , vol.38 , pp. 285-316
    • Wolkowicz, G.S.K.1    Xia, H.2    Wu, J.3
  • 33
    • 39649098899 scopus 로고    scopus 로고
    • Separate roles of the latent and infectious periods in shaping the relation between the basic reproduction number and the intrinsic growth rate of infectious disease outbreaks
    • P. Yan. Separate roles of the latent and infectious periods in shaping the relation between the basic reproduction number and the intrinsic growth rate of infectious disease outbreaks. J. Theoret. Biol., 251 (2008), 238-252.
    • (2008) J. Theoret. Biol. , vol.251 , pp. 238-252
    • Yan, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.