arXiv subjects

Gonzalo Marcelo Ramírez-Ávila

Publications and source records attributed to Gonzalo Marcelo Ramírez-Ávila.

3 recordsLinked to original sources

arXiv2026

Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane

We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynamical systems (DSs). Morphologically, they are characterized by a branch and a soma with several vertices (arms) and sometimes with multiple periodicities. A bunch of infinite astrocytes emerge through their branches from a region, in general, of low periodicity. Astrocytes are embedded in a quasiperiodic-chaotic scenario. The soma complexity (number of vertices) determines a kind of hierarchy of the astrocytes; moreover, bunches of subsequent structures from the astrocyte have been emphasized, revealing a self-similarity property. We conducted a detailed analysis in a Zeeman laser model, but we also observed astrocytes in many other DSs. The multiperiodicity exhibited by the astrocytes in their soma gives rise to harlequin dress-like patterns and tri-, quad-, and quint-critical points, which indicate the coexistence of different higher-order periodicities. In the concave borders of the soma, a doubling cascade of quint-points emerges as a bifurcation in the PP, defining regions of ordered sequences of higher periodicity in the route to chaos.

nlin.CD↗

arXiv2026

A Dynamical-Time Framework for the Dynamics of Charged Particles

We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical variable. The framework applies to the relativistic regime while consistently admitting a nonrelativistic limit. We also introduce a representation of particle trajectories in velocity space, which provides clear insight into the nature and asymptotic behavior of the dynamics. As an application, we compare the motion of massive and massless particles in a constant electromagnetic field and find that, for identical field configurations, their asymptotic behavior is independent of both mass and initial conditions. Finally, we explore the computational advantages of the dynamical-time formulation over the conventional uniform-time approach in two case studies: a uniform electromagnetic field, and an elliptically polarized wave propagating along a uniform magnetic field. In both scenarios, the proposed scheme exhibits improvements in accuracy and computational efficiency.

physics.class-ph↗

arXiv2016

Tweaking Synchronisation by Link Addition

Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behaviour. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either a discrete or continuous. Here our main result is that a certain amount of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.

nlin.CD↗