arXiv subjects

Juan P. Tarigo

Publications and source records attributed to Juan P. Tarigo.

4 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↗

arXiv2026

Phase-space organization of the elastic pendulum: chaotic fraction, energy exchanges, and the order-chaos-order transition

We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy $R$ and the squared frequency ratio $μ$. By randomly sampling the isoenergetic volume to classify trajectories as oscillatory, rotational, or chaotic across the $(μ, R)$ parameter plane, we obtain a global portrait of the coexistence and competition between dynamical regimes. The chaotic fraction is not uniformly distributed across the parameter plane but concentrates in a well-defined central cloud whose ridge follows a linear relation in the $(μ, R)$ plane and whose maximum does not exceed $70\%$ of the available phase space. The order-chaos-order transition is not a global property of the parameter plane but occurs specifically in the central region surrounding this cloud: along paths that traverse it, oscillatory orbits progressively give way to chaotic trajectories, which in turn yield to rotational orbits as the energy grows, revealing a clear sequential mechanism underlying the transition. The onset of rotational motion is gradual rather than sharp, reflecting a strong dependence on initial conditions. By decomposing the total energy into spring-like, pendulum-like, and coupling contributions, we establish a direct correspondence between the coupling power and the abundance of chaotic trajectories, showing that enhanced inter-mode energy exchange is a reliable indicator of dynamical complexity. These results provide a comprehensive and quantitative map of the dynamical regimes of the elastic pendulum, clarifying the structure of the chaotic cloud and connecting it to the underlying mode-coupling mechanisms.

nlin.CD↗

arXiv2024

Basin of attraction organization in infinite-dimensional delayed systems: a stochastic basin entropy approach

The Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of the long-term dynamics is especially challenging in these systems, where the dimensionality is infinite and initial conditions must be specified as a function in a finite time interval. In this paper we extend the recently proposed basin entropy to randomly sample arbitrarily high-dimensional spaces. By complementing this stochastic approach with the basin fraction of the attractors in the initial conditions space we can understand the structure of the basins of attraction and how they are intermixed. The results reported here allow us to quantify the predictability giving us an idea about the long-term evolution of trajectories as a function of the initial conditions. The tools employed can result very useful in the study of complex systems of infinite dimension.

nlin.CD↗

arXiv2021

Characterizing multistability regions in the parameter space of the Mackey-Glass delayed system

Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of the parameter space. This model can be represented by a dynamical system with a single variable obeying a delayed differential equation. Since it is infinite dimensional requires to specify a real function in a finite interval as an initial condition. Here, the dynamics of the Mackey-Glass model is investigated numerically using a scheme previously validated with experimental results. First, we explore the parameter space and describe regions in which solutions of different periodic or chaotic behaviors exist. Next, we show that the system presents regions of multistability, i.e. the coexistence of different solutions for the same parameter values but for different initial conditions. We remark the coexistence of periodic solutions with the same period but consisting of several maximums with the same amplitudes but in different orders. We characterize the multistability regions by introducing families of representative initial condition functions and evaluating the abundance of the coexisting solutions. These findings contribute to describe the complexity of this system and explore the possibility of possible applications such as to store or to code digital information.

cond-mat.dis-nn↗