The general recombination equation in continuous time and its solution

Baake E, Baake M, Salamat M (2016)
Discrete and Continuous Dynamical Systems 36(1): 63-95.

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Journal Article | Original Article | Published | English

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The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs that permits a systematic analysis with lattice-theoretic methods for general partitions of finite sets. We discuss this type of system, reduce it to an equivalent finite-dimensional nonlinear problem, and establish a connection with an ancestral partitioning process, backward in time. We solve the finite-dimensional problem recursively for generic sets of parameters and briefly discuss the singular cases, and how to extend the solution to this situation.
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Baake E, Baake M, Salamat M. The general recombination equation in continuous time and its solution. Discrete and Continuous Dynamical Systems. 2016;36(1):63-95.
Baake, E., Baake, M., & Salamat, M. (2016). The general recombination equation in continuous time and its solution. Discrete and Continuous Dynamical Systems, 36(1), 63-95. doi:10.3934/dcds.2016.36.63
Baake, E., Baake, M., and Salamat, M. (2016). The general recombination equation in continuous time and its solution. Discrete and Continuous Dynamical Systems 36, 63-95.
Baake, E., Baake, M., & Salamat, M., 2016. The general recombination equation in continuous time and its solution. Discrete and Continuous Dynamical Systems, 36(1), p 63-95.
E. Baake, M. Baake, and M. Salamat, “The general recombination equation in continuous time and its solution”, Discrete and Continuous Dynamical Systems, vol. 36, 2016, pp. 63-95.
Baake, E., Baake, M., Salamat, M.: The general recombination equation in continuous time and its solution. Discrete and Continuous Dynamical Systems. 36, 63-95 (2016).
Baake, Ellen, Baake, Michael, and Salamat, Majid. “The general recombination equation in continuous time and its solution”. Discrete and Continuous Dynamical Systems 36.1 (2016): 63-95.
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