Dynamics of Multimodal Families of m-Modal Maps

Javier Salvador González Salas Bahia Betzavet Cassal Quiroga JOSE TUXPAN VARGAS Eric Campos Cantón (2022)

"In this work, we introduce families of multimodal maps based on logistic map, i.e., families of m-modal maps are defined on an interval I C R, which is partitioned into non-uniform subdomains, with m E N. Because the subdomains of the partition are not uniform, each subdomain contains a unimodal map, given by the logistic map, that can have different heights. Therefore, we give the necessary and sufficient conditions for these modal maps present a multimodal family of m-modal maps, i.e., a bifurcation parameter can set a unimodal map, a bimodal map, up to a -modal map. Some numerical examples are given according to the developed theory. Some numerical examples are given in accordance with the developed theory."

Artículo

Chaos CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS MATEMÁTICAS

Deterministic Brownian-like Motion: Electronic Approach

JOSE LUIS ECHENAUSIA MONROY Eric Campos Cantón Rider Jaimes Reátegui JUAN HUGO GARCIA LOPEZ GUILLERMO HUERTA CUELLAR (2022)

"Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully deterministic set of differential equations. The dynamics of the electronic circuit are characterized using four well-known metrics of Brownian motion, namely: (i) Detrended Fluctuation Analysis (DFA), (ii) power law in the power spectrum, (iii) normal probability distribution, and (iv) Mean Square Displacement (MSD); where traditional Brownian motion exhibits linear time growth of the MSD, a Gaussian distribution, a −2 power law of the frequency spectrum, and DFA values close to 1.5. The obtained results show that for a certain combination of values in the deterministic model, the dynamics in the electronic circuit are consistent with the expectations for a stochastic Brownian behavior. The presented electronic circuit improves the study of Brownian behavior by eliminating the stochastic component, allowing reproducibility of the results through fully deterministic equations, and enabling the generation of physical signals (analog electronic signals) with Brownian-like properties with potential applications in fields such as medicine, economics, genetics, and communications, to name a few."

Artículo

Brownian motion Deterministic Brownian motion DFA analysis Statistical analysis Electronic circuit Electronic implementation CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA ELECTRÓNICA