arXiv subjects

Luis Guillermo Venegas-Pineda

Publications and source records attributed to Luis Guillermo Venegas-Pineda.

3 recordsLinked to original sources

arXiv2026

Strategic control for a Boltzmann like decision-making model

We study a prototypical non-polynomial decision-making model for which agents in a population potentially alternate between two consumption strategies, one related to the exploitation of an unlimited but considerably expensive resource and the other a comparably cheaper but restricted and slowly renewable source. In particular, we study a model following a Boltzmann-like exploration policy, enhancing the accuracy at which the exchange rates are captured with respect to classical polynomial approaches by considering sigmoidal functions to represent the cost-profit relation in both exploit strategies. Additionally, given the intrinsic timescale separation between the decision-making process and recovery rates of the renewable resource, we use geometric singular perturbation theory to analyze the model. We further use numerical analysis to determine parameter ranges for which the model undergoes bifurcations. These bifurcations, being related to critical states of the system, are relevant to the fast transitions between strategies. Hence, we design controllers to regulate such rapid transitions by taking advantage of the system's criticality.

math.DS↗

arXiv2025

Co-evolutionary control of a class of coupled mixed-feedback systems

Oscillatory behavior is ubiquitous in many natural and engineered systems, often emerging through self-regulating mechanisms. In this paper, we address the challenge of stabilizing a desired oscillatory pattern in a networked system where neither the internal dynamics nor the interconnections can be changed. To achieve this, we propose two distinct control strategies. The first requires the full knowledge of the system generating the desired oscillatory pattern, while the second only needs local error information. In addition, the controllers are implemented as co-evolutionary, or adaptive, rules of some edges in an extended plant-controller network. We validate our approach in several insightful scenarios, including synchronization and systems with time-varying network structures.

eess.SY↗

arXiv2023

Stable Chimera States: A Geometric Singular Perturbation Approach

Over the past decades chimera states have attracted considerable attention given their unexpected symmetry-breaking spatio-temporal nature, simultaneously exhibiting synchronous and incoherent behaviours under specific conditions. Despite relevant precursory results of such unforeseen states for diverse physical and topological configurations, there remain structures and mechanisms yet to be unveiled. In this work, using mean-field techniques, we analyze a multilayer network composed by two populations of heterogeneous Kuramoto phase oscillators with coevolutive coupling strengths. Moreover, we employ Geometric Singular Perturbation Theory (GSPT) with the inclusion of a time-scale separation between the dynamics of the network elements and the adaptive coupling strength connecting them, gaining a better insight into the behaviour of the system from a fast-slow dynamics perspective. Consequently, we derive the necessary and sufficient condition to produce stable chimera states when considering a co-evolutionary intercoupling strength. Additionally, under the aforementioned constraint and with a suitable adaptive law election, it is possible to generate intriguing patterns, such as persistent breathing chimera states. Thereafter, we analyze the geometric properties of the mean-field system with a co-evolutionary intracoupling strength and demonstrate the production of stable chimera states which depend on the associated network. Finally, relaxation oscillations and canard cycles, also related to breathing chimeras, are numerically produced under identified conditions due to the geometry of our system.

math.DS↗