arXiv subjects

Caracé Gutiérrez

Publications and source records attributed to Caracé Gutiérrez.

3 recordsLinked to original sources

arXiv2026

Experimental observation of chaotic and multistable dynamics in a Duffing--Holmes--type analog circuit: antiperiodicity and attractor-coexistence signatures

An experimental study of a periodically forced Duffing--Holmes-type oscillator with a double-well potential, emulated by a piecewise-linear analog electronic circuit, is presented. By systematically varying the forcing amplitude and frequency, the full dynamical landscape of the system is characterized through bifurcation diagrams, Poincaré maps, and largest Lyapunov exponent calculations. The observed phenomenology includes period-doubling routes to chaos, periodic windows with multistability, intermittency, and antiperiodic orbits in which the trajectory recovers the global symmetry of the double-well potential. Multistability-induced discontinuities in the bifurcation diagrams are identified and interpreted as attractor-coexistence signatures arising from the sensitivity of the long-time dynamics to initial conditions, rather than as noise artifacts. These results are synthesized into a high-resolution two-dimensional map of the parameter space. The close agreement among all experimental diagnostics validates the fidelity of this analog implementation and demonstrates that continuous-time hardware provides a high-throughput platform for mapping complex nonlinear landscapes and resolving fine-scale multistable structures.

nlin.CD↗

arXiv2020

Observation of bifurcations and hysteresis in experimentally coupled logistic maps

Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation cascades going from periodic to chaotic solutions. Studying coupled maps allows to identify other qualitative changes in the collective dynamics, such as pattern formations or hysteresis. Particularly, hysteresis is the appearance of different attracting sets, a set when the control parameter is increased and another set when it is decreased -- a multi-stable region. In this work, we present an experimental study on the bifurcations and hysteresis of nearly identical, coupled, logistic maps. Our logistic maps are an electronic system that has a discrete-time evolution with a high signal-to-noise ratio ($\sim10^6$), resulting in simple, precise, and reliable experimental manipulations, which include the design of a modifiable diffusive coupling configuration circuit. We find that the characterisations of the isolated and coupled logistic-maps' dynamics agrees excellently with the theoretical and numerical predictions (such as the critical bifurcation points and Feigenbaum's bifurcation velocity). Here, we report multi-stable regions appearing robustly across configurations, even though our configurations had parameter mismatch (which we measure directly from the components of the circuit and also infer from the resultant dynamics for each map) and were unavoidably affected by electronic noise.

nlin.AO↗

arXiv2020

Finding the Resistance Distance and Eigenvector Centrality from the Network's Eigenvalues

There are different measures to classify a network's data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological pathways and differentiating between biomedical images of patients with Alzheimer's disease, respectively. The resistance distance measures the effective distance between any two nodes of a network taking into account all possible shortest paths between them and the eigenvector centrality measures the relative importance of each node in the network. However, both measures require knowing the network's eigenvalues and eigenvectors -- eigenvectors being the more computationally demanding task. Here, we show that we can closely approximate these two measures using only the eigenvalue spectra, where we illustrate this by experimenting on elemental resistor circuits and paradigmatic network models -- random and small-world networks. Our results are supported by analytical derivations, showing that the eigenvector centrality can be perfectly matched in all cases whilst the resistance distance can be closely approximated. Our underlying approach is based on the work by Denton, Parke, Tao, and Zhang [arXiv:1908.03795 (2019)], which is unrestricted to these topological measures and can be applied to most problems requiring the calculation of eigenvectors.

physics.soc-ph↗