Modelling Complex Systems
Traditionally, mathematical models of biological systems have mostly been phenomenological because of the difficulty of deriving a set of equations from first principles in the way that can typically be done in the physical sciences. Sometimes, attempts are made to fit a parametrised model to data, but the fit is usually very bad and all that is hoped for is a qualitative understanding. Recent work in dynamical systems theory has made it possible to construct non-parametric models directly from data. This paper describes a particular approach—embedding followed by tesselation—which appears able to capture the main features of some biological systems, and to provide a degree of quantitative predictive power.
KeywordsStrange Attractor Dimensional Manifold Multivariate Adaptive Regression Spline Dynamical System Theory Original Time Series
Unable to display preview. Download preview PDF.
- M. Casdagli, Phys. Rev. Leiters, to appear. (1989).Google Scholar
- A. Fraser (1988), Information and entropy in strange attractors, IEEE Trans. Information Theory, in press.Google Scholar
- J.H. Friedman, Multivariate adaptive regression splines, Technical Report 102, Laboratory for Computational Statistics, Stanford University (1988).Google Scholar
- V. Guillemin and A. Pollack, Differential Topology, Prentice-Hall New Jersey (1974).Google Scholar
- A.I. Mees, Tesselations and Dynamical Systems, in preparation (1989).Google Scholar
- F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction, Springer, New York, (1985).Google Scholar
- P.E. Rapp, A.M. Albano and A.I. Mees, Calculation of correlation dimensions from experimental data: progress and problems. In Dynamic patterns in complex systems, eds. J.A.S. Kelso, A.J. Mandell and M.F. Schlesinger, pp. 191–205. World Scientific, Singapore (1988).Google Scholar
- B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London (1988).Google Scholar
- C.T. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Applied Mathematical Sciences 41, Springer, New York (1982).Google Scholar
- F. Takens, Dynamical Systems and Turbulence, Vol 898 of Lecture Notes in Mathematics, ed. D.A. Rand and L.-S. Young, page 366, Springer, Berlin (1981).Google Scholar