{"product_id":"model-emergent-dynamics-in-complex-systems-paperback-softback-9781611973556","title":"Model Emergent Dynamics in Complex Systems (Paperback \/ softback) 9781611973556","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eModel Emergent Dynamics in Complex Systems\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA book that explores the derivation of multiscale models for dynamical systems, partnering algebra and geometry with a visual approach.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eA.j. Roberts (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781611973556\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 December 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e760 pages\u003cbr\u003e25.8 x 18 x 3.8 cm, 1.354 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eArising from the growing interest in dynamical systems theory, this book explores the derivation of relatively simple dynamical equations that model complex physical interactions. It unifies into one coherent approach many varied extant methods for model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between multiscale models and paradoxes, and addresses model reduction for systems, resolves initial conditions, and illuminates control. The methodology focusses on the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems leading to a broad range of geometric interpretations of the modeling process that it produces. This facilitates an enhanced view of other modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, and WKB theory. Researchers at the graduate level and above who need to understand systems and modeling at different levels of resolution and complexity will find this book useful.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Asymptotic Methods Solve Algebraic and Differential Equations: 1. Perturbed algebraic equations solved iteratively\u003cbr\u003e 2. Power series solve ordinary differential equations\u003cbr\u003e 3. A normal form of oscillations illuminate their character\u003cbr\u003e Part I summary\u003cbr\u003e Part II. Center Manifolds Underpin Accurate Modeling: 4. The center manifold emerges\u003cbr\u003e 5. Construct slow center manifolds iteratively\u003cbr\u003e Part II summary\u003cbr\u003e Part III. Macroscale Spatial Variations Emerge from Microscale Dynamics: 6. Conservation underlies mathematical modeling of fluids\u003cbr\u003e 7. Cross-stream mixing causes longitudinal dispersion along pipes\u003cbr\u003e 8. Thin fluid films evolve slowly over space and time\u003cbr\u003e 9. Resolve inertia in thicker faster fluid films\u003cbr\u003e Part III summary\u003cbr\u003e Part IV. Normal Forms Illuminate Many Modeling Issues: 10. Normal-form transformations simplify evolution\u003cbr\u003e 11. Separating fast and slow dynamics proves modeling\u003cbr\u003e 12. Appropriate initial conditions empower accurate forecasts\u003cbr\u003e 13. Subcenter slow manifolds are useful but do not emerge\u003cbr\u003e Part IV summary\u003cbr\u003e Part V. High Fidelity Discrete Models Use Slow Manifolds: 14. Introduce holistic discretization on just two elements\u003cbr\u003e 15. Holistic discretization in one space dimension\u003cbr\u003e Part V summary\u003cbr\u003e Part VI. Hopf Bifurcation: Oscillations Within the Center Manifold: 16. Directly model oscillations in Cartesian-like variables\u003cbr\u003e 17. Model the modulation of oscillations\u003cbr\u003e Part VI summary\u003cbr\u003e Part VII. Avoid Memory in Modeling Nonautonomous Systems, Including Stochastic: 18. Averaging is often a good first modeling approximation\u003cbr\u003e 19. Coordinate transforms separate slow from fast in nonautonomous dynamics\u003cbr\u003e 20. Introducing basic stochastic calculus\u003cbr\u003e 21. Strong and weak models of stochastic dynamics\u003cbr\u003e Part VII summary\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52446331306264,"sku":"9781611973556","price":80.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781611973556i.jpg?v=1785111090","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/model-emergent-dynamics-in-complex-systems-paperback-softback-9781611973556","provider":"Freshly Printed Books","version":"1.0","type":"link"}