Systems of differential equations that are competitive or cooperative. VI: A local Cr Closing Lemma for 3-dimensional systems

A drive nut is mounted at one end of a load distributing carriage through which passes a threaded shaft which is fixed against rotation and engaged with said nut. The nut is rotationally driven about the shaft to cause the carriage to move up or down the shaft. An additional nut is carried by the shaft and connected to the drive nut for movement therewith. The additional nut is unloaded and provides a safety stop in the event of failure of the drive nut.

[1]  Max b. Müller.  Über das Fundamentaltheorem in der Theorie der gewöhnlichen Differentialgleichungen , 1927 .

[2]  E. Kamke.  Zur Theorie der Systeme gewöhnlicher Differentialgleichungen. II. , 1932 .

[3]  E. H. Kerner.  On the Volterra-Lotka principle , 1961 .

[4]  A Rescigno,et al.  The struggle for life: II. Three competitors , 1968 .

[5]  R. M. Arthur,et al.  Species packing, and what competition minimizes. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[6]  S. Levin.  Community Equilibria and Stability, and an Extension of the Competitive Exclusion Principle , 1970, The American Naturalist.

[7]  F. Albrecht,et al.  The dynamics of two interacting populations , 1974 .

[8]  M. Gilpin.  Limit Cycles in Competition Communities , 1975, The American Naturalist.

[9]  R. May,et al.  Nonlinear Aspects of Competition Between Three Species , 1975 .

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

[11]  John J. Tyson,et al.  The Dynamics of Feedback Control Circuits in Biochemical Pathways , 1978 .

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

[13]  J. Coste,et al.  About the theory of competing species. , 1978, Theoretical population biology.

[14]  P. Schuster,et al.  On $\omega $-Limits for Competition Between Three Species , 1979 .

[15]  J. Coste,et al.  Asymptotic Behaviors in the Dynamics of Competing Species , 1979 .

[16]  L. J. Svoboda,et al.  Persistence and extinction in three species Lotka-Volterra competitive systems , 1979 .

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

[18]  J. Peyraud,et al.  Strange attractors in volterra equations for species in competition , 1982, Journal of mathematical biology.

[19]  H. I. Freedman.  Deterministic mathematical models in population ecology , 1982 .

[20]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

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

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

[23]  J. Smillie.  Competitive and Cooperative Tridiagonal Systems of Differential Equations , 1984 .

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

[25]  V. Hutson,et al.  Permanent coexistence in general models of three interacting species , 1985, Journal of mathematical biology.

[26]  P. Schuster,et al.  An analytic study of the May-Leonard equations , 1985 .

[27]  J. Coste.  Dynamical Regression in Many Species Ecosystems: the Case of Many Predators Competing for Several Preys , 1985 .

[28]  H. I. Freedman,et al.  Persistence in a model of three competitive populations , 1985 .

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

[30]  Paul Waltman,et al.  Uniformly persistent systems , 1986 .

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

[32]  Hal L. Smith.  On the asymptotic behavior of a class of deterministic models of cooperating species , 1986 .

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