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Geometric dynamics of calcium oscillations ODEs systems. (English) Zbl 1077.37523

Summary: From a differential geometric point of view, this paper expresses in time dependent least squares Lagrangian terms that the solutions of any DE systems of order one are harmonic curves on 1-jet spaces. Natural time dependent electromagnetic fields, together with their generalized Maxwell equations, are derived from the given DE systems and suitable geometric structure. Important applications to biological DE systems governing the intracellular calcium oscillations in a model involving degradation of inositol triphosphate or calcium oscillations in a model that takes into account three stored in the cell (endoplasmic reticulum, mitochondria and cytosolic proteins), together with some natural biologic-electromagnetic Yang-Mills energies of geometric-physical type, are established. Some derived geometric-biological interpretations are exposed as well.

MSC:

37N25 Dynamical systems in biology
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
92C35 Physiological flow
53C80 Applications of global differential geometry to the sciences
34K20 Stability theory of functional-differential equations
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
83C22 Einstein-Maxwell equations
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