Global bifurcations in a simple, autocatalytic reaction

References

• Alfsen , K and Froyland , J . 1985 . Systematics of the Lorenz model at σ=10 . Physica Scripta , 31 : 15 – 20 .
   Web of Science ®Google Scholar
• Andronov , A , Leontovich , E , Gordon , I and Maier , A . 1971 . Theory of Bifurcations of Dynamic Systems on a Plane , Israel Program for Scientific Translations Jerusalem. .
   Google Scholar
• Doedel , E . 1986 . “ AUTO: Software for continuation and bifurcation problems in ordinary differential equations ” . California Institute of Technology .
   Google Scholar
• Golubitsky , M and Langford , W . 1981 . Classification and unfoldings of degenerate Hopf bifurcations . Journal of Differential Equations , 41 : 375 – 415 .
   Web of Science ®Google Scholar
• Gray , P and Scott , S . 1983 . Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability . Chemical Engineering Science , 38 : 29 – 43 .
   Web of Science ®Google Scholar
• Gray , P. and Scott , S.K. 1984 . Autocatalytic reactions in the continuous stirred tank in the system A + 2B→3B, B→C . Chemical Engineering Science , 39 : 1087 – 1097 .
   Web of Science ®Google Scholar
• Gray , P and Scott , S.K. 1985 . Sustained oscillations and other exotic patterns of behaviour in isothermal reactions . Journal of Physics and Chemistry , 89 : 22 – 32 .
   Web of Science ®Google Scholar
• Gray , P. and Scott , S.K. 1986 . A new model for oscillatory behaviour in closed systems . Berundt Bunsen Geshaft Physica Chemie , 90 : 985 – 996 .
   Web of Science ®Google Scholar
• Guckenheimer , J and Holmes , P . 1983 . “ Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Applied Mathematical Sciences ” . Vol. 42 , New York : Springer .
   Google Scholar
• Hassard , B and Wan , Y-H . 1978 . Bifurcation formulae derived from, centre manifold theory . Journal of Mathematical Analysis and Applications , 63 : 297 – 312 .
   Web of Science ®Google Scholar
• Hassard , B , Kazarinoff , N and Wan , Y-H . 1981 . Theory and Applications of Hopf Bifurcation , Vol. 41 , Cambridge : University Press . London Mathematical Society Lecture Notes
   Google Scholar
• Kay , S. R. and Needham , D . 1989 . Pattern formation in a simple autocatalytic reaction . In preparation , 41
   Google Scholar
• Kay , S and Scott , S . 1988 . Multiple stationary states, sustained oscillations and transient behaviour in autocatalytic reaction-diffusion equations . Proceedings of the Royal Society , A418 : 345 – 364 .
   Google Scholar
• Kay , S , Scott , S and Lignola , P-G . 1987 . The application of singularity theory to isothermal autocatalytic reactions: the influence of uncatalysed reactions . Proceedings of the Royal Society , A409 : 449 – 452 .
   Google Scholar
• Merkin , J , Needham , D and Scott , S . 1987 . On the creation, growth and extinction of oscillatory solutions for a simple pooled chemical reaction scheme . Proceedings of the Royal Society , A406 : 299 – 323 .
   Google Scholar