Alternate realities: mathematical models of nature and man
Praise for Alternate Realities Mathematical Models of Nature and Man "‚¶covers the major topics completely and accurately within the context of current knowledge. Indeed, to my knowledge, there is no book which does so nearly as completely and well." ‚George Leitmann, University of California, Berkeley "Surveys an extensive amount of modern mathematics‚¶introduces and outlines some of these basic modern ideas for the non-specialist." ‚Donald G. Saari, Northwestern University "A sophisticated and modern text on mathematical modelling‚¶much more comprehensive than any of its competitors currently on the market." ‚George Klir, State University of New York at Binghamton "Casti‚s approach is fearless in constructing conceptual mappings between reality and mathematical notions. The book is pioneering in nature." ‚Myron B. Allen, University of Wyoming
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Natural Systems and Formal Mathematical Representations 1 A Theory of Models
States Observables and Natural Systems
Equations of State
133 other sections not shown
assume attractor automaton basic behavior bifurcation brain catastrophe theory cell cellular automata chaos chaotic chapter characteristic values classical codimension complex components consider corresponding critical point cusp cycle defined discussion dynamical system elements encoding equation equilibrium equivalent evolution evolutionary example finite fixed point foregoing function gene genetic genotype geometry given global idea incidence matrix initial configuration input input/output interaction involving language linear system Lyapunov exponents manifold mathematical metabolic mixed strategy Moore neighborhood neighborhood nonzero notion observables one-dimensional optimal output parameters pattern payoff matrix phenotype physical players polynomial population possible problem properties quadratic question random reachable relation repair map replicator dynamics replicator systems represent result rule scientific sequence Show singularity theory situation smooth smooth functions Splitting Lemma stable state-space strategy structure vector subsystem Theorem time-steps tion trajectories variables