Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith

Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.

[1]  Y Takeuchi.  Diffusion-mediated persistence in two-species competition Lotka-Volterra model. , 1989, Mathematical biosciences.

[2]  Paul C. Fife,et al.  Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbances , 1981 .

[3]  P. Hess,et al.  Periodic-Parabolic Boundary Value Problems and Positivity , 1991 .

[4]  Paul Waltman,et al.  Persistence in dynamical systems , 1986 .

[5]  M. Kreĭn,et al.  Linear operators leaving invariant a cone in a Banach space , 1950 .

[6]  Hiroshi Matano,et al.  Convergence of solutions of one-dimensional semilinear parabolic equations , 1978 .

[7]  R. Martin,et al.  Reaction-diffusion systems with time delays: monotonicity, invariance, comparison and convergence. , 1991 .

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

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

[10]  G. Greiner,et al.  Zur Perron-Frobenius-Theorie stark stetiger Halbgruppen , 1981 .

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

[12]  Jiang Jifa,et al.  Attractors in strongly monotone flows , 1991 .

[13]  Xavier Mora,et al.  Semilinear parabolic problems define semiflows on ^{} spaces , 1983 .

[14]  R. Nagel,et al.  Asymptotic behavior of one-parameter semigroups of positive operators , 1984 .

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

[16]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[17]  Robert H. Martin,et al.  Nonlinear operators and differential equations in Banach spaces , 1976 .

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

[19]  Janusz Mierczyński,et al.  On monotone trajectories , 1991 .

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

[21]  B. C. Baltzis,et al.  The growth of pure and simple microbial competitors in a moving distributed medium. , 1992, Mathematical biosciences.

[22]  S. Grossberg.  Competition, Decision, and Consensus , 1978 .

[23]  R. B. Kellogg,et al.  On a differential equation arising from compartmental analysis , 1978 .

[24]  Yasuhiro Takeuchi,et al.  Permanence and global stability for competitive Lotka-Volterra diffusion systems , 1995 .

[25]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[26]  W. M. Post,et al.  Dynamics and comparative statics of mutualistic communities. , 1979, Journal of theoretical biology.

[27]  Paul Waltman,et al.  Competition in an n -vessel gradostat , 1991 .

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

[29]  Derek W. Robinson,et al.  Positive one-parameter semigroups on ordered banach spaces , 1984 .

[30]  R. Robinson,et al.  Stability theorems and hyperbolicity in dynamical systems , 1977 .

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

[32]  S. P. Blythe,et al.  Nicholson's blowflies revisited , 1980, Nature.

[33]  Pierre-Louis Lions,et al.  Structure of the set of steady-state solutions and asymptotic behaviour of semilinear heat equations , 1984 .

[34]  Robert Gardner.  Comparison and Stability Theorems for Reaction-Diffusion Systems , 1981 .

[35]  H. Amann.  Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces , 1976 .

[36]  W. Gurney,et al.  Modelling fluctuating populations , 1982 .

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

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

[39]  Horst R. Thieme,et al.  Convergence for strongly order-preserving semiflows , 1991 .

[40]  Hal L. Smith,et al.  Abstract functional-differential equations and reaction-diffusion systems , 1990 .

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

[42]  Chris Cosner,et al.  Should a Park Be an Island? , 1993, SIAM J. Appl. Math..

[43]  Hal L. Smith.  Cooperative systems of differential equations with concave nonlinearities , 1986 .

[44]  Hal L. Smith,et al.  Competition in the gradostat: the role of the communication rate , 1989 .

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

[46]  G. Seifert,et al.  Positively invariant closed sets for systems of delay differential equations , 1976 .

[47]  Jianhong Wu,et al.  Global Dynamics of Strongly Monotone Retarded Equations with Infinite Delay , 1992 .

[48]  K. P. Hadeler,et al.  Quasimonotone systems and convergence to equilibrium in a population genetic model , 1983 .

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

[50]  B. S. Goh,et al.  Stability in Models of Mutualism , 1979, The American Naturalist.

[51]  Horst R. Thieme,et al.  Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations , 1992 .

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

[53]  S. Tuljapurkar,et al.  Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomathematics, Volume 28.Paul C. Fife , S. Levin , 1980 .

[54]  Peter Takáč,et al.  Asymptotic behavior of discrete-time semigroups of sublinear, strongly increasing mappings with applications to biology , 1990 .

[55]  Y. Ohta,et al.  Qualitative analysis of nonlinear quasi-monotone dynamical systems described by functional-differential equations , 1981 .

[56]  Jianhong Wu,et al.  Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems , 1991, Canadian Journal of Mathematics.

[57]  Maria Assunta Pozio.  Decay estimates for partial functional differential equations , 1982 .

[58]  Peter N. Brown,et al.  Decay to Uniform States in Ecological Interactions , 1980 .

[59]  Sze-Bi Hsu,et al.  Analysis of a model of two competitors in a chemostat with an external inhibitor , 1992 .

[60]  E. D. Conway,et al.  A comparison technique for systems of reaction-diffusion equations , 1977 .

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

[62]  H. Bruce Stewart,et al.  Generation of analytic semigroups by strongly elliptic operators under general boundary conditions , 1980 .

[63]  K. P. Hadeler,et al.  Periodic solutions of difference-differential equations , 1977 .

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

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

[66]  Anthony W. Leung,et al.  Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering , 1989 .

[67]  James F. Selgrade,et al.  Asymptotic behavior of solutions to single loop positive feedback systems , 1980 .

[68]  O. Ladyzhenskaya,et al.  Attractors for Semigroups and Evolution Equations , 1991 .

[69]  W. Walter.  Differential and Integral Inequalities , 1970 .

[70]  P. Polácik,et al.  Convergence in smooth strongly monotone flows defined by semilinear parabolic equations , 1989 .

[71]  A. Friedman.  Partial Differential Equations of Parabolic Type , 1983 .

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

[73]  Paul Waltman,et al.  A nonlinear boundary value problem arising from competition in the chemostat , 1989 .

[74]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .