## The predator-prey model: do we live in a Volterra world?This book studies the phenomena of growth and structure building. It demonstrates that most of the macromodels described by sets of ordinary differential equations can be transformed into a presentation by the Lotka-Volterra Equation, the basic equation of ecology. |

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### Contents

Growth and StructureBuilding | 1 |

EVOLON | 29 |

Dynamic Behaviour of Chains | 53 |

Copyright | |

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### Common terms and phrases

additional state-variables approach assume autocatalytic base module behaviour biomass cluster coefficients computation concept consider construction convergence convex cone corresponding determined driving forces dx/dt dxjdt dynamic ecological elements equivalence transformations EVOLON model evolution example exponent exponential chain exponential growth expression finite following form function fuzzy generalised given graph growth indicator growth model growth process growth rate hyperbolic growth hypercycle of order hyperlogistic differential equation IIASA increase initial values INPUT integration interaction introduce linear systems linearly independent logarithmic derivative logistic Lotka Lotka-Volterra equations Lotka-Volterra representation Lotka-Volterra system matrix meaning monotonous monotonous functions motion multinomial differential equation nonlinear normalisation condition Obviously operator ordinary differential equations parameters positive cone possible PRINT problem rate-coupling realisation replicator equation restrict result Riccati representation robust ROM's saturation shift-cone signal simulation solution species step structure design principle structure design process structure-building Taylor chains tion trajectory variables vector Volterra XI X2