1. Contrasting chaotic with stochastic dynamics via ordinal transition networks
- Author
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Olivares, F., Zanin, M., Zunino, Luciano José, and Pérez, D.G.
- Subjects
Dynamical systems theory ,Series (mathematics) ,Plane (geometry) ,Computer science ,Applied Mathematics ,Numerical analysis ,NONLINEAR DYNAMICS ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,purl.org/becyt/ford/1.3 [https] ,Complex network ,01 natural sciences ,STOCHASTIC PROCESSES ,010305 fluids & plasmas ,purl.org/becyt/ford/1 [https] ,Position (vector) ,0103 physical sciences ,CHAOS ,010306 general physics ,Representation (mathematics) ,Algorithm ,Mathematical Physics - Abstract
We introduce a representation space to contrast chaotic with stochastic dynamics. Following the complex network representation of a time series through ordinal pattern transitions, we propose to assign each system a position in a two-dimensional plane defined by the permutation entropy of the network (global network quantifier) and the minimum value of the permutation entropy of the nodes (local network quantifier). The numerical analysis of representative chaotic maps and stochastic systems shows that the proposed approach is able to distinguish linear from non-linear dynamical systems by different planar locations. Additionally, we show that this characterization is robust when observational noise is considered. Experimental applications allow us to validate the numerical findings and to conclude that this approach is useful in practical contexts. We introduce a representation space to contrast chaotic with stochastic dynamics. Following the complex network representation of a time series through ordinal pattern transitions, we propose to assign each system a position in a two-dimensional plane defined by the permutation entropy of the network (global network quantifier) and the minimum value of the permutation entropy of the nodes (local network quantifier). The numerical analysis of representative chaotic maps and stochastic systems shows that the proposed approach is able to distinguish linear from non-linear dynamical systems by different planar locations. Additionally, we show that this characterization is robust when observational noise is considered. Experimental applications allow us to validate the numerical findings and to conclude that this approach is useful in practical contexts. Fil: Olivares, F.. Pontificia Universidad Católica de Valparaíso; Chile Fil: Olivares, F.. Pontificia Universidad Católica de Valparaíso; Chile Fil: Zanin, M.. Universidad Politécnica de Madrid; España Fil: Zanin, M.. Universidad Politécnica de Madrid; España Fil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Ciencias Básicas; Argentina Fil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Ciencias Básicas; Argentina Fil: Pérez, D.G.. Pontificia Universidad Católica de Valparaíso; Chile Fil: Pérez, D.G.. Pontificia Universidad Católica de Valparaíso; Chile
- Published
- 2020
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