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Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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• Reference Manager
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• RefWorks (Direct export to RefWorks)

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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The description for this book, Advances in Game Theory. (AM-52), Volume 52, will be forthcoming.

Game theory. --- Almost surely. --- Automorphism. --- Axiom. --- Basis (linear algebra). --- Bayesian probability. --- Big O notation. --- Bounded set (topological vector space). --- Calculation. --- Cartesian product. --- Characteristic function (probability theory). --- Complete theory. --- Conditional probability distribution. --- Continuous function (set theory). --- Continuum hypothesis. --- Cooperative game. --- Coset. --- Counterexample. --- Cumulative distribution function. --- Decision rule. --- Decision-making. --- Determinacy. --- Diagram (category theory). --- Differential game. --- Distribution function. --- Dyadic rational. --- Equation solving. --- Equation. --- Equilibrium point. --- Estimation. --- Existence theorem. --- Family of sets. --- Foundations of mathematics. --- Function (mathematics). --- Fundamental theorem. --- Game show. --- Hamilton–Jacobi equation. --- Harmonic function. --- Independence (probability theory). --- Inequality (mathematics). --- Infimum and supremum. --- Initial value problem. --- Invertible matrix. --- Jacobian matrix and determinant. --- Joint probability distribution. --- Linear inequality. --- Linear map. --- Linear programming. --- Lipschitz continuity. --- Markov chain. --- Markov process. --- Markov property. --- Mathematical analysis. --- Mathematical economics. --- Mathematical induction. --- Mathematical optimization. --- Matrix (mathematics). --- Minimax theorem. --- Minor (linear algebra). --- Mutual exclusivity. --- N-vector. --- Open set. --- Outcome (probability). --- Parity (mathematics). --- Partially ordered set. --- Payment. --- Permutation. --- Preference (economics). --- Prime number. --- Primitive root modulo n. --- Probability distribution function. --- Probability distribution. --- Probability measure. --- Probability. --- Quantifier (logic). --- Quantity. --- Random variable. --- Randomization. --- Ranking (information retrieval). --- Representation theory. --- Sample space. --- Scientific notation. --- Search game. --- Set (mathematics). --- Shapley value. --- Simultaneous equations. --- Skew-symmetric matrix. --- Solution concept. --- Special case. --- Strategy (game theory). --- Subset. --- Summation. --- Superadditivity. --- Sylow theorems. --- Theorem. --- Theory of Games and Economic Behavior. --- Theory. --- Topology. --- Utility. --- Variable (mathematics). --- Weighted arithmetic mean.

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A new group of contributions to the development of this theory by leading experts in the field. The contributors include L. D. Berkovitz, L. E. Dubins, H. Everett, W. H. Fleming, D. Gale, D. Gillette, S. Karlin, J. G. Kemeny, R. Restrepo, H. E. Scarf, M. Sion, G. L. Thompson, P. Wolfe, and others.

Game theory. --- Almost surely. --- American Mathematical Society. --- Axiom of choice. --- Bayes estimator. --- Big O notation. --- Binomial coefficient. --- Binomial theorem. --- Boundary value problem. --- C0. --- Calculation. --- Cartesian product. --- Characteristic function (probability theory). --- Coefficient. --- Complete metric space. --- Composition series. --- Continuous function (set theory). --- Continuous game. --- Counterexample. --- Decision problem. --- Decision theory. --- Determinacy. --- Diagram (category theory). --- Differential equation. --- Differential game. --- Distribution function. --- Elementary matrix. --- Equation. --- Existence theorem. --- Expected utility hypothesis. --- Extended real number line. --- Family of sets. --- Finitary. --- Function (mathematics). --- Functional equation. --- Fundamenta Mathematicae. --- Fundamental theorem. --- Inequality (mathematics). --- Infimum and supremum. --- Integral equation. --- Interval (mathematics). --- Joint probability distribution. --- Kakutani fixed-point theorem. --- Kakutani's theorem. --- Laplace's equation. --- Lipschitz continuity. --- Loss function. --- Markov chain. --- Martingale (probability theory). --- Mathematical analysis. --- Mathematical induction. --- Mathematical optimization. --- Mathematics. --- Maxima and minima. --- Measure (mathematics). --- Metric space. --- Monotonic function. --- N-vector. --- Ordinal number. --- Outcome (probability). --- Parametric statistics. --- Parity (mathematics). --- Partial differential equation. --- Polynomial. --- Preference (economics). --- Probability distribution. --- Probability measure. --- Probability theory. --- Probability. --- Product topology. --- Proportionality (mathematics). --- Randomization. --- Rate of convergence. --- Real projective plane. --- Recurrence relation. --- Recursive set. --- Recursively enumerable set. --- Reductio ad absurdum. --- Restriction (mathematics). --- Scientific notation. --- Series (mathematics). --- Set (mathematics). --- Sigma-algebra. --- Sign (mathematics). --- Solution set. --- Special case. --- Stochastic game. --- Stochastic process. --- Stochastic. --- Strategy (game theory). --- Subharmonic function. --- Summation. --- Theorem. --- Topological game. --- Topological space. --- Topology. --- Transfinite induction. --- Turing machine. --- Utility. --- Variable (mathematics). --- Zorn's lemma.