Brian Dennis – författare

It is impossible to predict the exact behavior of all biological systems and how these same systems are exemplified by patterns of complexity and regularity. Decades of research in ecology have documented how these sorts of patterns are the consequences of deceptively simple rules that determine the nature of the patterns created. Chaos in Ecology will explain how simple beginnings result in complicated results.

Chaos in Ecology is the inaugural volume of Theoretical Ecology Series. The authors of this volume have employed data from a proven model system in population dynamics. As a result, this book will be of interest to anyone interested in the ecology of populations.

Complex Population Dynamics: Theory and Data brings together over two decades of research and reflection on experimental nonlinear population dynamics. The broad theme of the book is the interface of population data and mathematical models. The authors establish a cornerstone example of a low-dimensional mathematical population model for which quantitative predictions, often unexpected, were borne out in controlled and replicated experiments. Central messages include the importance of low-dimensional, mechanistic models that serve as testable hypotheses; the importance of model validation on independent data; the prediction of novel outcomes in response to parameter manipulation; the interaction of nonlinearity and stochasticity—and how stochasticity illuminates, rather than obscures, deterministic forces; abrupt transitions in dynamic regimes in response to interventions; and how chaotic dynamics are expressed in discrete-state, noisy population systems. The book explores nonlinear phenomena in experimental data, including equilibria, cycles, bifurcations, invariant loops, multiple attractors, resonance and attenuance, saddles, stable and unstable manifolds, basins of attraction, basin boundaries, and chaos, and shows how these dynamics manifest in real data in both time series and state space plots.

The book offers an invaluable resource to professional ecologists and applied mathematicians. Although primarily a reference text, it is written to be accessible and engaging to a student audience and could be used as supplementary reading in an advanced ecological modeling class.

Features

Complex Population Dynamics: Theory and Data brings together over two decades of research and reflection on experimental nonlinear population dynamics. The broad theme of the book is the interface of population data and mathematical models. The authors establish a cornerstone example of a low-dimensional mathematical population model for which quantitative predictions, often unexpected, were borne out in controlled and replicated experiments. Central messages include the importance of low-dimensional, mechanistic models that serve as testable hypotheses; the importance of model validation on independent data; the prediction of novel outcomes in response to parameter manipulation; the interaction of nonlinearity and stochasticity—and how stochasticity illuminates, rather than obscures, deterministic forces; abrupt transitions in dynamic regimes in response to interventions; and how chaotic dynamics are expressed in discrete-state, noisy population systems. The book explores nonlinear phenomena in experimental data, including equilibria, cycles, bifurcations, invariant loops, multiple attractors, resonance and attenuance, saddles, stable and unstable manifolds, basins of attraction, basin boundaries, and chaos, and shows how these dynamics manifest in real data in both time series and state space plots.

The book offers an invaluable resource to professional ecologists and applied mathematicians. Although primarily a reference text, it is written to be accessible and engaging to a student audience and could be used as supplementary reading in an advanced ecological modeling class.

Features

The fact that surprisingly few Christians actually know and experience the mighty God we preach about, teach about, and sing about is evidenced by the abundance of doubt, worry, and fear that permeate our lives. It is evidenced by the lack of faith and power exemplified in our Churches. It is evidenced by the ordinary lives we live while claiming to be children of the most high God. The resulting inconsistencies between the things we boldly profess and the things we commonly practice have unfortunately become accepted as normal Christian behavior. We no longer expect anything more--not from our own lives, not from the Church, not even from God Himself.

This lack of expectancy, this lack of faith in the faithfulness of God clearly indicates a distinct difference between the God we preach and the God we have personally come to know. It reveals that we do not know the very God we proclaim. We do not know the God of the Bible; for if we knew Him, the Church would indeed be an eminent light shining in the darkness, a city set on a hill, an indelible force against which the powers of this present evil world could not prevail.

The God we do know, however, the God with whom so many Christians have become familiar, unfortunately, allows us to live comfortably in the weakness of our complacency and blatant disbelief. We live far below the high calling that Christ has placed upon His Church. We walk in ways that deny the very power and authority that belong to the children of God. We do not live by faith. Sadly, we have learned to live in such a way as to where there is no distinguishable difference between the lives of those who claim to know Christ and the lives of those who do not--no distinguishable difference between the Church and the world.

The good news is that the truth remains. The God of the Bible is still there. He can do no other than prove Himself faithful to those who hunger and thirst after righteousness--to those who hear His voice and obey. Yes, to those who would yet have a heart to know Him, He is there to be known. We must first, however, lay aside all notions of the small God we have come to know and we must dare to see Him as He is if we are to rise above the routine of cultural Christianity and walk in the truth of knowing Christ.