Understanding Nonlinear DynamicsSpringer Science & Business Media, 2012 M12 6 - 420 páginas Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors. |
Contenido
1 | |
BOOLEAN NETWORKS AND CELLULAR | 56 |
Locomotion in Salamanders | 70 |
ONEDIMENSIONAL DIFFERENTIAL | 147 |
Open Time Histograms in Patch Clamp Experiments | 158 |
TWODIMENSIONAL DIFFERENTIAL | 209 |
37 | 252 |
TIMESERIES ANALYSIS | 279 |
55 | 345 |
APPENDIX A A MULTIFUNCTIONAL APPENDIX | 359 |
The Sine and Cosine Functions | 367 |
APPENDIX B A NOTE ON COMPUTER | 381 |
BIBLIOGRAPHY | 401 |
409 | |
412 | |
Reconstructing Nerve Cell Dynamics | 304 |
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Términos y frases comunes
action potential algebraic amplitude analysis approximately assume attractor autocorrelation function behavior Boolean C₁ calculate called cells cellular automata chaos Chapter correlation correlation dimension correlation integral curve cycle of period D₁ data from Model derivative described determine deterministic discriminating statistic dx dt dynamical system DYNAMICS IN ACTION eigenvalues embedding dimension example exponential decay exponential growth finite-difference equation fractal frequency geometry given graph initial condition input integral iteration k₁ linear dynamics Lotka-Volterra equations mathematical mean measurement noise Mest method Model Four Model Three molecules N₁ node nonlinear null hypothesis one-dimensional ordinary differential equations original oscillations output parameters phase plane plot population prediction random number saddle point self-similar sensitive dependence shown in Figure shows sigmoidal function sine wave slope solution standard deviation steady surrogate data trajectory tumor two-dimensional unstable V₁ V₁+1 variables versus white noise x₁ Xt+1 y-isocline zero