Self-similarities of periodic structures for a discrete model of a two-gene system |
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| Authors: | S.L.T. de Souza,A.A. Lima,I.L. Caldas,R.O. Medrano-T.,Z.O. Guimarã es-Filho |
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| Affiliation: | 1. Departamento de Física e Matemática, Universidade Federal de São João del-Rei, Ouro Branco, MG, Brazil;2. Escola de Farmácia, Universidade Federal de Ouro Preto, Ouro Preto, MG, Brazil;3. Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil;4. Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, SP, Brazil;5. Aix-Marseille Univ., CNRS PIIM UMR6633, International Institute for Fusion Science, Marseille, France |
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| Abstract: | We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. |
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| Keywords: | Arnold tongues Shrimps Golden ratio Lyapunov exponents Two-gene model |
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