Nature's Patterns and the Fractional Calculus

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, complexit...

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Main Author West, Bruce J
Format eBook
LanguageEnglish
Published Berlin/Boston Walter de Gruyter GmbH 2017
De Gruyter
Edition1
SeriesFractional Calculus in Applied Sciences and Engineering
Subjects
Allometry
Fractional calculus
MATHEMATICS / Complex Analysis
Mathematics in nature
pattern formation
Pattern formation (Biology)
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Abstract 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
AbstractList 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
Complexity increases with increasing system size in everything from organisms to organisations. 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.
Author West, Bruce J
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Snippet Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its...
Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system's functionality on its...
Complexity increases with increasing system size in everything from organisms to organisations. The nonlinear dependence of a system's functionality on its...
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SubjectTerms Allometry
Fractional calculus
MATHEMATICS / Complex Analysis
Mathematics in nature
pattern formation
Pattern formation (Biology)
TableOfContents Intro -- Foreword -- Acknowledgement -- Contents -- 1. Complexity -- 2. Empirical allometry -- 3. Statistics, scaling and simulation -- 4. Allometry theories -- 5. Strange kinetics -- 6. Fractional probability calculus -- Epilogue -- Bibliography -- Index
3. Statistics, scaling and simulation --
Contents --
Epilogue --
2. Empirical allometry --
Acknowledgement --
Index
Foreword --
1. Complexity --
5. Strange kinetics --
6. Fractional probability calculus --
Frontmatter --
4. Allometry theories --
Bibliography --
Title Nature's Patterns and the Fractional Calculus
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