An optimization framework of biological dynamical systems

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1 Citation (Scopus)


Different biological dynamics are often described by different mathematical equations. On the other hand, some mathematical models describe many biological dynamics universally. Here, we focus on three biological dynamics: the Lotka-Volterra equation, the Hopfield neural networks, and the replicator equation. We describe these three dynamical models using a single optimization framework, which is constructed with employing the Riemannian geometry. Then, we show that the optimization structures of these dynamics are identical, and the differences among the three dynamics are only in the constraints of the optimization. From this perspective, we discuss the unified view for biological dynamics. We also discuss the plausible categorizations, the fundamental nature, and the efficient modeling of the biological dynamics, which arise from the optimization perspective of the dynamical systems.

Original languageEnglish
Pages (from-to)45-54
Number of pages10
JournalJournal of Theoretical Biology
Issue number1
Publication statusPublished - 2008 Jul 7
Externally publishedYes


  • Constrained optimization
  • Hopfield neural networks
  • Lotka-Volterra equation
  • Replicator equation
  • Riemannian geometry

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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