Geodesic
Geometric characteristics of cycles in some symmetric dynamical systems
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 3-12

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We show non-uniqueness of cycles in phase portraits of some odd-dimensional nonlinear dynamical systems considered as models of gene networks regulated by negative feedbacks. We find geometric and analytic characteristics of these cycles and construct a graph, which describes qualitative behavior of trajectories of these dynamical systems.
Keywords: gene networks models, nonlinear dynamical systems, stationary points, periodic trajectories, unstable cycles, graphs, numerical modeling.
Mots-clés : invariant domains 
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     author = {A. A. Akinshin and V. P. Golubyatnikov},
     title = {Geometric characteristics of cycles in some symmetric dynamical systems},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {3--12},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a0/}
}
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A. A. Akinshin; V. P. Golubyatnikov. Geometric characteristics of cycles in some symmetric dynamical systems. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 3-12. http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a0/