Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models

[1]  Mauro Mobilia,et al.  Fluctuations and correlations in lattice models for predator-prey interaction. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  U. Tauber,et al.  TOPICAL REVIEW: Applications of field-theoretic renormalization group methods to reaction diffusion problems , 2005, cond-mat/0501678.

[3]  A J McKane,et al.  Predator-prey cycles from resonant amplification of demographic stochasticity. , 2005, Physical review letters.

[4]  H. Janssen,et al.  The field theory approach to percolation processes , 2004, cond-mat/0409670.

[5]  E. Albano,et al.  A self-organized system of smart preys and predators , 2004 .

[6]  H. Hilhorst,et al.  Segregation in diffusion-limited multispecies pair annihilation , 2004, cond-mat/0403246.

[7]  György Szabó,et al.  Phase transition and selection in a four-species cyclic predator-prey model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Dick Neal,et al.  Introduction to Population Biology , 2018 .

[9]  Adam Lipowski,et al.  Oscillations and dynamics in a two-dimensional prey-predator system. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  H. Hilhorst,et al.  Multispecies pair annihilation reactions. , 2002, Physical review letters.

[11]  A. Provata,et al.  Fractal properties of the lattice Lotka-Volterra model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  G. Ódor,et al.  Hard core particle exclusion effects in low dimensional non-equilibrium phase transitions , 2001, cond-mat/0109399.

[13]  H. Janssen.  Directed Percolation with Colors and Flavors , 2001 .

[14]  E V Albano,et al.  Critical and oscillatory behavior of a system of smart preys and predators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  M. Droz,et al.  Coexistence in a predator-prey system. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  G Szabó,et al.  Defensive alliances in spatial models of cyclical population interactions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Mobilia,et al.  Soluble two-species diffusion-limited models in arbitrary dimensions. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  T. Antal,et al.  Phase transitions and oscillations in a lattice prey-predator model. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  “Quantum phase transitions” in classical nonequilibrium processes , 1999, cond-mat/9908450.

[20]  F. Wijland.  Field theory for reaction-diffusion processes with hard-core particles. , 2000, cond-mat/0010491.

[21]  Study of interacting particle systems: the transition to the oscillatory behavior of a prey–predator model , 2000 .

[22]  Adam Lipowski,et al.  Nonequilibrium phase transition in a lattice prey–predator system , 2000 .

[23]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[24]  Rick Durrett,et al.  Stochastic Spatial Models , 1999, SIAM Rev..

[25]  A Lipowski,et al.  Oscillatory behavior in a lattice prey-predator system. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Grégoire Nicolis,et al.  Oscillatory dynamics in low-dimensional supports: A lattice Lotka–Volterra model , 1999 .

[27]  Ezequiel V. Albano,et al.  Study of a lattice-gas model for a prey–predator system , 1999 .

[28]  H. Levine,et al.  Interfacial velocity corrections due to multiplicative noise , 1998, cond-mat/9811020.

[29]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[30]  Book Review: Nonequilibrium Statistical Mechanics in One Dimension , 1999 .

[31]  D. Mattis,et al.  The uses of quantum field theory in diffusion-limited reactions , 1998 .

[32]  P. Krapivsky,et al.  Fixation in a cyclic Lotka-Volterra model , 1998, cond-mat/9801026.

[33]  Ricard V. Solé,et al.  Modeling spatiotemporal dynamics in ecology , 1998 .

[34]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[35]  M. Wadati,et al.  Reaction-Diffusion Processes with Multi-Species of Particles , 1997 .

[36]  Jaime E. Santos,et al.  Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains , 1996, cond-mat/9610059.

[37]  Iwan Jensen,et al.  Low-density series expansions for directed percolation on square and triangular lattices , 1996 .

[38]  Ben-Naim,et al.  Segregation in a One-Dimensional Model of Interacting Species. , 1996, Physical review letters.

[39]  R. May,et al.  Metapopulations and equilibrium stability: the effects of spatial structure. , 1996, Journal of theoretical biology.

[40]  Ben-Naim,et al.  Spatial organization in cyclic Lotka-Volterra systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  Riordan,et al.  Fluctuations and stability of fisher waves. , 1995, Physical review letters.

[42]  Roblin,et al.  Automata network predator-prey model with pursuit and evasion. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  Tomé,et al.  Stochastic lattice gas model for a predator-prey system. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[44]  Akira Sasaki,et al.  Statistical Mechanics of Population: The Lattice Lotka-Volterra Model , 1992 .

[45]  Akira Sasaki,et al.  Statistical Mechanics of Population , 1992 .

[46]  R. May,et al.  Population regulation and dynamics : proceedings of a Royal Society Discussion Meeting, held on 23 and 24 May 1990 , 1990 .

[47]  H. Haken,et al.  Synergetics , 1988, IEEE Circuits and Devices Magazine.

[48]  Steven R. Dunbar,et al.  Travelling wave solutions of diffusive Lotka-Volterra equations , 1983 .

[49]  Peter Grassberger,et al.  On phase transitions in Schlögl's second model , 1982 .

[50]  T. Johnston,et al.  Instability Cascades, Lotka-Volterra Population Equations, and Hamiltonian Chaos , 1982 .

[51]  H. Janssen,et al.  On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state , 1981 .

[52]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[53]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[54]  R. May,et al.  Nonlinear Aspects of Competition Between Three Species , 1975 .

[55]  S. Jørgensen.  Models in Ecology , 1975 .

[56]  Elliott W. Montroll,et al.  Nonlinear Population Dynamics. (Book Reviews: On the Volterra and Other Nonlinear Models of Interacting Populations) , 1971 .

[57]  D. Denton.  The Royal Society of London , 1965, Nature.

[58]  C. Elton,et al.  The Ten-Year Cycle in Numbers of the Lynx in Canada , 1942 .

[59]  Vito Volterra,et al.  Leçons sur la théorie mathématique de la lutte pour la vie , 1931 .

[60]  A. J. Lotka.  UNDAMPED OSCILLATIONS DERIVED FROM THE LAW OF MASS ACTION. , 1920 .

[61]  A. J. Lotka.  Analytical Note on Certain Rhythmic Relations in Organic Systems , 1920, Proceedings of the National Academy of Sciences.