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Transversality for time-periodic competitive-cooperative tridiagonal systems
1. | Wu Wen-Tsun Key Laboratory, School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, China, China |
References:
[1] |
C. Fang, M. Gyllenberg and Y. Wang, Floquet bundles for tridiagonal competitive-cooperative systems and the dynamics of time-recurrent systems,, SIAM J. Math. Anal., 45 (2013), 2477.
doi: 10.1137/120878021. |
[2] |
G. Fusco and W. Oliva, Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems,, J. Dynam. Differential Equations, 2 (1990), 1.
doi: 10.1007/BF01047768. |
[3] |
G. Fusco and W. Oliva, Jacobi matrices and transversality,, Proc. Roy. Soc. Edinburgh Sect. A, 109 (1988), 231.
doi: 10.1017/S0308210500027748. |
[4] |
J. Hale and A. Somolinos, Competition for fluctuating nutrient,, J. Math. Biol., 18 (1983), 255.
doi: 10.1007/BF00276091. |
[5] |
M. Hirsch, Systems of differential equations that are competitive or cooperative. V. Convergence in 3-dimensional systems,, J. Differential Equations, 80 (1989), 94.
doi: 10.1016/0022-0396(89)90097-1. |
[6] |
J. Mallet-Paret and G. Sell, Systems of differential delay equations: Floquet multipliers and discrete lyapunov functions,, J. Dynam. Differential Equations, 125 (1996), 385.
doi: 10.1006/jdeq.1996.0036. |
[7] |
J. Mallet-Paret and H. Smith, The poincare-bendixson theorem for monotone cyclic feedback systems,, J. Dynam. Differential Equations, 2 (1990), 367.
doi: 10.1007/BF01054041. |
[8] |
P. Mottoni and A. Schiaffino, Competition systems with periodic coefficients: A geometric approach,, J. Math. Biol., 11 (1981), 319.
doi: 10.1007/BF00276900. |
[9] |
J. Selgrade, Isolated invariant sets for flows on vector bundles,, Trans. Amer. Math. Soc., 203 (1975), 359.
doi: 10.1090/S0002-9947-1975-0368080-X. |
[10] |
J. Smillie, Competitive and cooperative tridiagonal systems of differential equations,, SIAM J. Math. Anal., 15 (1984), 530.
doi: 10.1137/0515040. |
[11] |
H. Smith, Periodic tridiagonal competitive and cooperative systems of differential equations,, SIAM J. Math. Anal., 22 (1991), 1102.
doi: 10.1137/0522071. |
[12] |
Y. Wang, Dynamics of nonautonomous tridiagonal competitive-cooperative systems of differential equations,, Nonlinearity, 20 (2007), 831.
doi: 10.1088/0951-7715/20/4/002. |
show all references
References:
[1] |
C. Fang, M. Gyllenberg and Y. Wang, Floquet bundles for tridiagonal competitive-cooperative systems and the dynamics of time-recurrent systems,, SIAM J. Math. Anal., 45 (2013), 2477.
doi: 10.1137/120878021. |
[2] |
G. Fusco and W. Oliva, Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems,, J. Dynam. Differential Equations, 2 (1990), 1.
doi: 10.1007/BF01047768. |
[3] |
G. Fusco and W. Oliva, Jacobi matrices and transversality,, Proc. Roy. Soc. Edinburgh Sect. A, 109 (1988), 231.
doi: 10.1017/S0308210500027748. |
[4] |
J. Hale and A. Somolinos, Competition for fluctuating nutrient,, J. Math. Biol., 18 (1983), 255.
doi: 10.1007/BF00276091. |
[5] |
M. Hirsch, Systems of differential equations that are competitive or cooperative. V. Convergence in 3-dimensional systems,, J. Differential Equations, 80 (1989), 94.
doi: 10.1016/0022-0396(89)90097-1. |
[6] |
J. Mallet-Paret and G. Sell, Systems of differential delay equations: Floquet multipliers and discrete lyapunov functions,, J. Dynam. Differential Equations, 125 (1996), 385.
doi: 10.1006/jdeq.1996.0036. |
[7] |
J. Mallet-Paret and H. Smith, The poincare-bendixson theorem for monotone cyclic feedback systems,, J. Dynam. Differential Equations, 2 (1990), 367.
doi: 10.1007/BF01054041. |
[8] |
P. Mottoni and A. Schiaffino, Competition systems with periodic coefficients: A geometric approach,, J. Math. Biol., 11 (1981), 319.
doi: 10.1007/BF00276900. |
[9] |
J. Selgrade, Isolated invariant sets for flows on vector bundles,, Trans. Amer. Math. Soc., 203 (1975), 359.
doi: 10.1090/S0002-9947-1975-0368080-X. |
[10] |
J. Smillie, Competitive and cooperative tridiagonal systems of differential equations,, SIAM J. Math. Anal., 15 (1984), 530.
doi: 10.1137/0515040. |
[11] |
H. Smith, Periodic tridiagonal competitive and cooperative systems of differential equations,, SIAM J. Math. Anal., 22 (1991), 1102.
doi: 10.1137/0522071. |
[12] |
Y. Wang, Dynamics of nonautonomous tridiagonal competitive-cooperative systems of differential equations,, Nonlinearity, 20 (2007), 831.
doi: 10.1088/0951-7715/20/4/002. |
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