Dynamics of competition

[1]  Dongmei Xiao,et al.  Limit Cycles for the Competitive Three Dimensional Lotka–Volterra System , 2000 .

[2]  P. Polácik,et al.  Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems , 1992 .

[3]  Hal L. Smith.  Complicated dynamics for low-dimensional strongly monotone maps , 1997 .

[4]  Hal L. Smith.  Periodic solutions of periodic competitive and cooperative systems , 1986 .

[5]  Paul Waltman,et al.  A classification theorem for three dimensional competitive systems , 1987 .

[6]  C. Conley.  The gradient structure of a flow: I , 1988, Ergodic Theory and Dynamical Systems.

[7]  P. de Mottoni,et al.  Competition systems with periodic coefficients: A geometric approach , 1981 .

[8]  G. Harrison,et al.  Comparing Predator‐Prey Models to Luckinbill's Experiment with Didinium and Paramecium , 1995 .

[9]  Anthony W. Leung,et al.  Systems of Nonlinear Partial Differential Equations , 1989 .

[10]  Hal L. Smith,et al.  Stable Periodic Orbits for a Class of Three Dimensional Competitive Systems , 1994 .

[11]  Morris W. Hirsch,et al.  System of differential equations that are competitive or cooperative. IV: structural stability in three-dimensional systems , 1990 .

[12]  D. Hoff,et al.  LARGE TIME BEHAVIOR OF SOLUTIONS OF SYSTEMS OF NONLINEAR REACTION-DIFFUSION EQUATIONS* , 1978 .

[13]  Morris W. Hirsch,et al.  Systems of differential equations that are competitive or cooperative. VI: A local Cr Closing Lemma for 3-dimensional systems , 1991 .

[14]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[15]  Effect of domain-shape on coexistence problems in a competition-diffusion system , 1991 .

[16]  E. N. Dancer,et al.  Stability of fixed points for order-preserving discrete-time dynamical systems. , 1991 .

[17]  F. V. Vleck,et al.  Stability and Asymptotic Behavior of Differential Equations , 1965 .

[18]  Hal L. Smith.  The periodically forced Droop model for phytoplankton growth in a chemostat , 1997 .

[19]  Alan C. Lazer,et al.  On an abstract competition model and applications , 1991 .

[20]  Paul Waltman,et al.  The Theory of the Chemostat , 1995 .

[21]  Sze-Bi Hsu,et al.  Competitive exclusion and coexistence for competitive systems on ordered Banach spaces , 1996 .

[22]  Hal L. Smith.  Periodic competitive differential equations and the discrete dynamics of competitive maps , 1986 .

[23]  M. Hirsch.  Systems of differential equations that are competitive or cooperative. VI: A local Cr Closing Lemma for 3-dimensional systems , 1985, Ergodic Theory and Dynamical Systems.

[24]  William Gurney,et al.  Modelling fluctuating populations , 1982 .

[25]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[26]  E. J. McShane,et al.  Extension of range of functions , 1934 .

[27]  M. Hirsch.  The dynamical systems approach to differential equations , 1984 .

[28]  L. Luckinbill,et al.  Coexistence in Laboratory Populations of Paramecium Aurelia and Its Predator Didinium Nasutum , 1973 .

[29]  M V Makarets,et al.  SYSTEMS OF DIFFERENTIAL EQUATIONS , 1995 .

[30]  Hiroshi Matano,et al.  Pattern Formation in Competition-Diffusion Systems in Nonconvex Domains , 1983 .

[31]  M. Hirsch.  Stability and convergence in strongly monotone dynamical systems. , 1988 .

[32]  M. Hirsch.  Systems of differential equations that are competitive or cooperative. VI: A local Cr Closing Lemma for 3-dimensional systems , 1985, Ergodic Theory and Dynamical Systems.

[33]  Mary Lou Zeeman,et al.  Hopf bifurcations in competitive three-dimensional Lotka-Volterra Systems , 1993 .

[34]  A Goldbeter,et al.  Unified mechanism for relay and oscillation of cyclic AMP in Dictyostelium discoideum. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Jack K. Hale,et al.  Persistence in infinite-dimensional systems , 1989 .

[36]  Shair Ahmad,et al.  Asymptotic behaviour of solutions of periodic competition diffusion system , 1989 .

[37]  Kazuo Kishimoto,et al.  The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains , 1985 .

[38]  M. Pascual.  Periodic response to periodic forcing of the Droop equations for phytoplankton growth , 1994 .

[39]  Chia-Ven Pao,et al.  Nonlinear parabolic and elliptic equations , 1993 .

[40]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[41]  A. Goldbeter,et al.  Biochemical Oscillations And Cellular Rhythms: Contents , 1996 .

[42]  M. Hirsch.  Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere , 1985 .

[43]  S. Smale.  On the differential equations of species in competition , 1976, Journal of mathematical biology.

[44]  Josef Hofbauer,et al.  Multiple limit cycles for three dimensional Lotka-Volterra equations , 1994 .

[45]  Leping Zhou,et al.  Asymptotic behavior of a competition—diffusion system in population dynamics , 1982 .

[46]  Hal L. Smith,et al.  Competition for a Single Limiting Resource in Continuous Culture: The Variable-Yield Model , 1994, SIAM J. Appl. Math..

[47]  C. Conley.  Isolated Invariant Sets and the Morse Index , 1978 .

[48]  V. Capasso.  Mathematical Structures of Epidemic Systems , 1993, Lecture Notes in Biomathematics.

[49]  Hal L. Smith.  Periodic orbits of competitive and cooperative systems , 1986 .

[50]  M. Hirsch.  Systems of di erential equations which are competitive or cooperative I: limit sets , 1982 .

[51]  F. H. Jackson.  q-Difference Equations , 1910 .

[52]  J. K. Hale,et al.  Competition for fluctuating nutrient , 1983 .

[53]  Horst R. Thieme,et al.  Persistence under relaxed point-dissipativity (with application to an endemic model) , 1993 .

[54]  H. Weinberger,et al.  Maximum principles in differential equations , 1967 .

[55]  Y. Morita.  Reaction-diffusion systems in nonconvex domains: Invariant manifold and reduced form , 1990 .

[56]  Lee A. Segel,et al.  Modeling Dynamic Phenomena in Molecular and Cellular Biology , 1984 .