This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or epidemics. After reviewing the assumptions and mean-field type approximations involved in the construction of chemical rate equations for uniform reactant densities, we first discuss spatial clustering in birth-death systems, where non-linearities are introduced through either density-limiting pair reactions, or equivalently via local imposition of finite carrying capacities. The competition of offspring production, death, and non-linear inhibition induces a population extinction threshold, which represents a non-equilibrium phase transition that separates active from absorbing states. This continuous transition is characterized by the universal scaling exponents of critical directed percolation clusters. Next we focus on the emergence of depletion zones in single-species annihilation processes and spatial population segregation with the associated reaction fronts in two-species pair annihilation. These strong (anti-)correlation effects are dynamically generated by the underlying stochastic kinetics. Finally, we address noise-induced and fluctuation-stabilized spatio-temporal patterns in basic predator-prey systems, exemplified by spreading activity fronts in the two-species Lotka-Volterra model as well as spiral structures in the May-Leonard variant of cyclically competing three-species s...
Correlation Effects Two-species Lotka-Volterra Model Rock-paper-scissors Chemical Rate Equations Birth-death Systems Non-equilibrium Phase Transition Annihilation Stochastic Kinetics Extinction Threshold Percolation
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Round-ups are the summaries of handpicked papers around trending topics published every week. These would enable you to scan through a collection of papers and decide if the paper is relevant to you before actually investing time into reading it.
Climate change Research Articles published between Jan 23, 2023 to Jan 29, 2023
Jan 30, 2023
Articles Included: 3
Climate change adaptation has shifted from a single-dimension to an integrative approach that aligns with vulnerability and resilience concepts. Adapt...Read More
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