Nature’s Patterns and the Fractional Calculus

Inbunden, Engelska, 2017

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Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. ContentsComplexityEmpirical allometryStatistics, scaling and simulationAllometry theoriesStrange kineticsFractional probability calculus

Produktinformation

Utgivningsdatum2017-09-11
Mått170 x 240 x 18 mm
Vikt505 g
FormatInbunden
SpråkEngelska
SerieFractional Calculus in Applied Sciences and Engineering
Antal sidor213
Upplaga17001
FörlagDe Gruyter
ISBN9783110534115

Tillhör följande kategorier

Tillämpad matematik inom Naturvetenskap och teknik
Matematisk fysik inom Naturvetenskap och teknik
Anatomi inom Medicin
Biologi inom Naturvetenskap och teknik
Beräkning och matematisk analys inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Människans biologi inom Naturvetenskap och teknik
Fysiologi inom Medicin

Table of Content: Chapter 1: Complexity Science 1.1 It started with physics 1.2 Complexity 1.3 Measures of size 1.4 Allometry heuristics 1.5 Overview Chapter 2: Empirical Allometry 2.1 Living networks 2.2 Physical networks 2.3 Natural history 2.4 Sociology 2.5 Summary Chapter 3 Statistics, Scaling and Simulation 3.1 Interpreting fluctuations 3.2 Phenomenological distributions 3.3 Are ARs universal? 3.4 Summary Chapter 4: Models & Derivations of ARs 4.1 Optimization principles 4.2 Scaling and allometry 4.3 Stochastic differential equations 4.4 Fokker-Planck equations 4.5 Summary Chapter 5: Complex and Strange Kinetics 5.1 Fractional thinking 5.2 Fractional rate equations 5.3 Fractional Poisson process 5.4 A closer look at complexity 5.5 Recapitulation 5.6 Appendix Chapter 6: Fractional Probability Calculus 6.1 Fractional Fokker-Planck equation 6.2 Fully fractional phase space equations 6.3 Entropy entails allometry 6.4 Statistics of allometry parameters 6.5 Discussion and conclusions 6.6 Epilogue

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