메뉴 건너뛰기




Volumn 9, Issue 2, 2008, Pages 397-413

A two-parameter geometrical criteria for delay differential equations

Author keywords

Delay dependent parameters; Delay differential equations; Double hopf bifurcation; Geometrical criterion; Hopf bifurcation; Stability

Indexed keywords


EID: 67349150279     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (12)

References (20)
  • 1
    • 0003517776 scopus 로고    scopus 로고
    • Mathematical models in the applied sciences
    • Cambridge University Press, Cambridge
    • A. C. Fowler, "Mathematical Models in the Applied Sciences," Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1997.
    • (1997) Cambridge Texts in Applied Mathematics
    • Fowler, A.C.1
  • 4
    • 0003199186 scopus 로고
    • Retarded dynamical systems: Stability and characteristic functions
    • Longman, Essex
    • G. Stśpén, "Retarded Dynamical Systems: Stability and Characteristic Functions," Pitman Research Notes in Mathematics, Vol.210, Longman, Essex, 1989.
    • (1989) Pitman Research Notes in Mathematics , vol.210
    • Stśpén, G.1
  • 5
    • 0003798166 scopus 로고    scopus 로고
    • Theoretical problems in cavity nonlinear optics
    • Cambridge University Press, Cambridge
    • P. Mandel, "Theoretical Problems in Cavity Nonlinear Optics," Cambridge Studies in Modern Optics, Cambridge University Press, Cambridge, 1997.
    • (1997) Cambridge Studies in Modern Optics
    • Mandel, P.1
  • 6
    • 0001407970 scopus 로고    scopus 로고
    • Analysis of optimal velocity model with explicit delay
    • M. Bando, K. Hasebe, K. Nakanishi and A. Nakayama, Analysis of optimal velocity model with explicit delay, Phys. Rev. E, 58 (1998), 5429-5435.
    • (1998) Phys. Rev. e , vol.58 , pp. 5429-5435
    • Bando, M.1    Hasebe, K.2    Nakanishi, K.3    Nakayama, A.4
  • 7
    • 0037365558 scopus 로고    scopus 로고
    • Modifications of the optimal velocity traffic model to include delay due to driver reaction time
    • L. C. Davis, Modifications of the optimal velocity traffic model to include delay due to driver reaction time, Phys. A, 319 (2003), 557-567.
    • (2003) Phys. A , vol.319 , pp. 557-567
    • Davis, L.C.1
  • 8
    • 0001687872 scopus 로고
    • A model of stage structured population growth with density dependent time delay
    • W. G. Aiello, H. I. Freedman and J. Wu, A model of stage structured population growth with density dependent time delay, SIAM J. Appl. Math., 52 (1992), 855-869.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 855-869
    • Aiello, W.G.1    Freedman, H.I.2    Wu, J.3
  • 9
    • 0024900429 scopus 로고
    • Space-limited recruitment in open systems: The importance of time delays
    • J. R. Bence and R. M. Nisbet, Space-limited recruitment in open systems: the importance of time delays, Ecology, 70 (1989), 1434-1441.
    • (1989) Ecology , vol.70 , pp. 1434-1441
    • Bence, J.R.1    Nisbet, R.M.2
  • 10
    • 0002784039 scopus 로고    scopus 로고
    • Modeling and analysis of a marine bacteriophage infection with latency period
    • Real World Applications
    • E. Beretta and Y. Kuang, Modeling and analysis of a marine bacteriophage infection with latency period, Nonlin. Anal. (Real World Applications), 2 (2001), 35-74.
    • (2001) Nonlin. Anal. , vol.2 , pp. 35-74
    • Beretta, E.1    Kuang, Y.2
  • 11
    • 0033209987 scopus 로고    scopus 로고
    • Interaction of maturation delay and nonlinear birth in population and epidemic models
    • K. L. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, 3. Math. Biol., 39 (1999), 332-352.
    • (1999) Math. Biol. , vol.39 , pp. 332-352
    • Cooke, K.L.1    Van Den Driessche, P.2    Zou, X.3
  • 12
    • 0029521324 scopus 로고
    • Analysis of a delayed two-stage population model with space-limited recruitment
    • Y. Kuang and J. W. H. So, Analysis of a delayed two-stage population model with space-limited recruitment, SIAM J. Appl. Math., 55 (1995), 1675-1696.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 1675-1696
    • Kuang, Y.1    So, J.W.H.2
  • 14
    • 0037947648 scopus 로고    scopus 로고
    • Effects of time delayed position feedback on a van der Pol-Duffing oscillator
    • J. Xu and K. W. Chung, Effects of time delayed position feedback on a van der Pol-Duffing oscillator, Phys. D, 180 (2003), 17-39.
    • (2003) Phys. D , vol.180 , pp. 17-39
    • Xu, J.1    Chung, K.W.2
  • 15
    • 0007790565 scopus 로고    scopus 로고
    • Delay-independent stability of retarded dynamic systems of multiple degrees of freedom
    • Z. H. Wang and H. Y. Hu, Delay-independent stability of retarded dynamic systems of multiple degrees of freedom, 3. Sound and Vibration, 226 (1999), 57-81.
    • (1999) Sound and Vibration , vol.226 , pp. 57-81
    • Wang, Z.H.1    Hu, H.Y.2
  • 16
    • 0036373967 scopus 로고    scopus 로고
    • Geometric stability switch criteria in delay differential systems with delay dependent parameters
    • E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 1144-1165.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1144-1165
    • Beretta, E.1    Kuang, Y.2
  • 18
    • 0010351336 scopus 로고    scopus 로고
    • Stability with respect to the delay: On a paper of K. L. Cooke and P. van den Driessche
    • F. G. Boese, Stability with Respect to the Delay: On a paper of K. L. Cooke and P. van den Driessche, J. Math. Anal. Appl., 228 (1998), 293-321.
    • (1998) J. Math. Anal. Appl., 228 , pp. 293-321
    • Boese, F.G.1
  • 19
    • 23844460516 scopus 로고    scopus 로고
    • Dynamics of a logistic population model with maturation delay and nonlinear birth rate
    • S. Q. Ma, Q. S. Lu and S. L. Mei, Dynamics of a logistic population model with maturation delay and nonlinear birth rate, Discrete Cont. Dyn. Sys.-B, 5 (2005), 735-752.
    • (2005) Discrete Cont. Dyn. Sys.-B , vol.5 , pp. 735-752
    • Ma, S.Q.1    Lu, Q.S.2    Mei, S.L.3
  • 20
    • 70350646041 scopus 로고    scopus 로고
    • Double hopf bifurcation for van der pol-duffing oscillator with nonlinear delay feedback parameter
    • Vibration and Control in China, Bejing
    • S. Q. Ma and Q. S. Lu, Double Hopf Bifurcation for Van Der Pol-Duffing Oscillator with Nonlinear Delay Feedback Parameter, Proceedings of 2nd International Conference on Dynamics, Vibration and Control in China, Bejing, 2006.
    • (2006) Proceedings of 2nd International Conference on Dynamics
    • Ma, S.Q.1    Lu, Q.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.