Author | Jeffries, Clark. author |
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Title | Mathematical Modeling in Ecology [electronic resource] : A Workbook for Students / by Clark Jeffries |
Imprint | Boston, MA : Birkhรคuser Boston, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4550-6 |
Descript | X, 194 p. online resource |
One-An Introduction to Dynamical Systems as Models -- 1.1 Ecosystem Development in Terms of Ecology -- 1.2 State Space, or How to Add Apples and Oranges -- 1.3 Dynamical Systems as Treasure Hunts -- Two-Simple Difference Equation Models -- 2.1 Predator-Prey Difference Equation Dynamical Systems -- 2.2 Probabilistic Limit Cycles -- Three-Formalizing the Notion of Stability -- 3.1 The Concept of Ecosystem Stability -- 3.2 The Relation of Difference and Differential Equations -- 3.3 Limit Cycles -- 3.4 Lyapunov Theory -- 3.5 The Trapping of Trajectories -- Four-Introduction to Ecosystem Models -- 4.1 Brewing Beer and Yeast Population Dynamics -- 4.2 Attractor Trajectories -- 4.3 Derivatives of System Functions -- 4.4 The Linearization Theorem -- 4.5 The Hurwitz Stability Test -- Five-Introduction to Ecosystem Models -- 5.1 The Community Matrix -- 5.2 Predator-Prey Equations and Generalizations Thereof -- 5.3 Signed Digraphs -- 5.4 Qualitative Stability of Linear Systems -- Six-Qualitative Stability of Ecosystem Models -- 6.1 Qualitative Results in Modeling -- 6.2 Holistic Ecosystem Models -- 6.3 Holistic Ecosystem Models with Attractor Trajectories -- Seven-The Behavior of Models with Attractor Regions -- 7.1 Attractor Regions -- 7.2 The Lorenz Model -- 7.3 Elementary Ecosystem Models with Chaotic Dynamics -- Eight-Holistic Ecosystem Models with Attractor Regions -- 8.1 An Attractor Region Theorem -- 8.2 An Example -- Nine-Sequencing Energy Flow Models to Account for Shortgrass Prairie Energy Dynamics -- 9.1 Energy Flow and Accumulation Modeling -- 9.2 Accumulation Modeling -- 9.3 Estimating Energy Flows -- 9.4 Equations and Trajectories -- 9.5 Stability