Singularity Theory
and
Bifurcation Theory
Catastrophe theory, Math. Chronicle 5 (1977) 140-165.
[with T.Poston] Nonlinear modelling of multistable perception, Behavioral Science (special issue on catastrophe theory) 23 (1978) 318-334.
Catastrophe theory and equations of state: conditions for a butterfly singularity, Math. Proc. Camb. Phil. Soc. 88 (1980) 429-449.
[with A.E.R.Woodcock] On Zeeman's equations for the nerve impulse, Bull. Math. Biol. 43 (1981) 279-325.
Bifurcation and hysteresis varieties for the thermal-chainbranching model with a negative modal parameter, Math. Proc. Camb. Phil. Soc. 90 (1981) 127-139.
Applications of catastrophe theory to the physical sciences, Physica D 2 (1981) 245-305.
Catastrophe theory in physics, Rep. Progr. Physics 45 (1982) 185-221.
Progress in catastrophe theory, Report of Conference on Dynamic Nonlinear Theory and General Urban/Regional Systems, Washington DC 1981, Univ. of Kansas 1982, 367-376.
[with P. Peregoy] Catastrophe theory modelling in psychology, Psych. Bull. 94 (1983) 336-362.
Catastrophe-theoretic and dynamical systems modelling in social science: state of the art and prospects, in Catastrophe Theory: State of the Art and Potential Applications, F.C.Johnson and R.C.Lacher, ONR Report NR 170-938 (1983) 16-32.
Overview of catastrophe theory, in Catastrophe Theory: State of the Art and Potential Applications, F.C.Johnson and R.C.Lacher, ONR Report NR 170-938 (1983) 9-14.
Elementary catastrophe theory, IEEE Trans. Circuits & Systems 30 (1983) 578-586.
Non-elementary catastrophe theory, IEEE Trans. Circuits & Systems 30 (1983) 663-670.
Applications of non-elementary catastrophe theory, IEEE Trans. Circuits & Systems 31 (1984) 165-174.
[with G. Dangelmayr] Unfolding and classification of sequential bifurcations, SIAM J. Math. Anal. 15 (1984) 423-445.
[with A.E.R.Woodcock] Bifurcation and hysteresis varieties for the thermal-chainbranching model II: positive modal parameter, Math. Proc. Camb. Phil. Soc. 96 (1984) 331-349.
Beyond elementary catastrophe theory, Appl. Math. Comp. 14 (1984) 25-32.
[with G.Dangelmayr] Sequential bifurcations in continuous stirred tank reactors coupled in series, SIAM J. Appl. Math. 45 (1985) 895-917.
[with S.Janeczko] Symplectic singularities and optical diffraction, in Singularity Theory and its Applications — Warwick 1989, Part II: Singularities, Bifurcations, and Dynamics (eds. M.Roberts and I.Stewart), Lecture Notes in Mathematics 1463, Springer-Verlag, Heidelberg 1991, 220-255.
[with J.E.Furter and A.M.Sitta] Singularity theory and equivariant bifurcation problems with parameter symmetry, Math. Proc. Camb. Phil. Soc. 120 (1996) 547-578.
[with J.E.Furter and A.M.Sitta] Algebraic path formulation for equivariant bifurcation problems, Math. Proc. Camb. Phil. Soc. 124 (1998) 275-304.
[with M.Manoel] Degenerate bifurcations with Z2+Z2-symmetry, Internat. J. Bif. Chaos 9 (1999) 1653-1667.
[with M.Manoel] The classification of bifurcations with hidden symmetries, Proc. London Math. Soc. 80 (2000) 198-234.
[with A.P.S. Dias] Secondary bifurcations in systems with all-to-all coupling, Proc. Roy. Soc. Lond. A 459 (2003) 1969-1986.
[With M. Golubitsky, F. Antoneli, Z. Huang, and Y. Wang] Input-output networks, singularity theory, and homeostasis, in Advances in Dynamics, Optimzation and Computation (eds. O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle), Studies in Systems, Decision and Control 304,Springer, Berlin 2020, 31–65.
and
Bifurcation Theory
Catastrophe theory, Math. Chronicle 5 (1977) 140-165.
[with T.Poston] Nonlinear modelling of multistable perception, Behavioral Science (special issue on catastrophe theory) 23 (1978) 318-334.
Catastrophe theory and equations of state: conditions for a butterfly singularity, Math. Proc. Camb. Phil. Soc. 88 (1980) 429-449.
[with A.E.R.Woodcock] On Zeeman's equations for the nerve impulse, Bull. Math. Biol. 43 (1981) 279-325.
Bifurcation and hysteresis varieties for the thermal-chainbranching model with a negative modal parameter, Math. Proc. Camb. Phil. Soc. 90 (1981) 127-139.
Applications of catastrophe theory to the physical sciences, Physica D 2 (1981) 245-305.
Catastrophe theory in physics, Rep. Progr. Physics 45 (1982) 185-221.
Progress in catastrophe theory, Report of Conference on Dynamic Nonlinear Theory and General Urban/Regional Systems, Washington DC 1981, Univ. of Kansas 1982, 367-376.
[with P. Peregoy] Catastrophe theory modelling in psychology, Psych. Bull. 94 (1983) 336-362.
Catastrophe-theoretic and dynamical systems modelling in social science: state of the art and prospects, in Catastrophe Theory: State of the Art and Potential Applications, F.C.Johnson and R.C.Lacher, ONR Report NR 170-938 (1983) 16-32.
Overview of catastrophe theory, in Catastrophe Theory: State of the Art and Potential Applications, F.C.Johnson and R.C.Lacher, ONR Report NR 170-938 (1983) 9-14.
Elementary catastrophe theory, IEEE Trans. Circuits & Systems 30 (1983) 578-586.
Non-elementary catastrophe theory, IEEE Trans. Circuits & Systems 30 (1983) 663-670.
Applications of non-elementary catastrophe theory, IEEE Trans. Circuits & Systems 31 (1984) 165-174.
[with G. Dangelmayr] Unfolding and classification of sequential bifurcations, SIAM J. Math. Anal. 15 (1984) 423-445.
[with A.E.R.Woodcock] Bifurcation and hysteresis varieties for the thermal-chainbranching model II: positive modal parameter, Math. Proc. Camb. Phil. Soc. 96 (1984) 331-349.
Beyond elementary catastrophe theory, Appl. Math. Comp. 14 (1984) 25-32.
[with G.Dangelmayr] Sequential bifurcations in continuous stirred tank reactors coupled in series, SIAM J. Appl. Math. 45 (1985) 895-917.
[with S.Janeczko] Symplectic singularities and optical diffraction, in Singularity Theory and its Applications — Warwick 1989, Part II: Singularities, Bifurcations, and Dynamics (eds. M.Roberts and I.Stewart), Lecture Notes in Mathematics 1463, Springer-Verlag, Heidelberg 1991, 220-255.
[with J.E.Furter and A.M.Sitta] Singularity theory and equivariant bifurcation problems with parameter symmetry, Math. Proc. Camb. Phil. Soc. 120 (1996) 547-578.
[with J.E.Furter and A.M.Sitta] Algebraic path formulation for equivariant bifurcation problems, Math. Proc. Camb. Phil. Soc. 124 (1998) 275-304.
[with M.Manoel] Degenerate bifurcations with Z2+Z2-symmetry, Internat. J. Bif. Chaos 9 (1999) 1653-1667.
[with M.Manoel] The classification of bifurcations with hidden symmetries, Proc. London Math. Soc. 80 (2000) 198-234.
[with A.P.S. Dias] Secondary bifurcations in systems with all-to-all coupling, Proc. Roy. Soc. Lond. A 459 (2003) 1969-1986.
[With M. Golubitsky, F. Antoneli, Z. Huang, and Y. Wang] Input-output networks, singularity theory, and homeostasis, in Advances in Dynamics, Optimzation and Computation (eds. O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle), Studies in Systems, Decision and Control 304,Springer, Berlin 2020, 31–65.
