APPENDIX AN INTUITIVE GUIDE TO THE IDEAS AND METHODS OF DYNAMICAL SYSTEMS FOR THE LIFE SCIENCES Arnold J. Mandell and Karen A. Selz Biological Scientists Can Understand and Use Ideas and Methods of Nonlinear Science A yield of advances in computer hardware and software is that even quite difficult applied nonlinear mathematics can become accessible to experimentally oriented biological scientists. Before this time, the development and analysis of a particular set of nonlinear differential equations, describing the actions of a neurobiological system in motion, involved decades of specialty training, rare insight and many hours of highly skilled, trial and error computations by hand. Since the idiosyncrasies of each nonlinear system were considered unique, the results of their analyses were thought to concern only the particular nonlinear system being studied. Often a shift in hypothetical mechanism meant starting the long and painful process all over again. In addition, these findings were usually communicated only to a small and arcane mathematical community in the form of dense theorems and difficult to follow proofs, insurmountable language barriers to biological researchers wishing to use them to better describe and understand their experimental observations. For today’s neuroscientist with a desktop computer, an inclination to program and access to computer algebra and numerical software such as Maple, Mathematica or MatLab, operational definitions and computational empiricism can replace the theorem and proof continuity required to do old style applied mathematics. For those of us without sufficient facility in algebraic manipulation to easily follow the arguments of professional mathematicians, a computer algebra program such as Maple serves as a delightfully accessible consultant with which to “check out what the guy is saying". Those motivated enough to write their own data generating or analytic programs in C, Fortran, Pascal or Basic (though not 186 HO