# gst: how mobile oscillators reshape dynamical robustness in complex networks.

<< ️While the robustness of collective dynamics in static networks is well established, how agent mobility and network topology jointly shape dynamical robustness remains largely unexplored. >>

<< ️In this letter, (AA) investigate the robustness of mobile Stuart-Landau oscillators performing random walks on networks and interacting diffusively when co-located. In the rapid-mobility regime, (They) reduce the dynamics to a mean-field framework linking network degree statistics to an effective global coupling strength. >> 

<< ️(AA) show analytically that increased degree heterogeneity in the network enhances the effective coupling strength, and strictly lowers the critical threshold of functional degradation for amplitude death. Numerical simulations confirm the predicted heterogeneity-dependent ordering of the transition thresholds, showing an earlier collective collapse in scale-free networks than in random or regular networks. >> 

<< ️(Their) results establish mobility and network heterogeneity as key determinants of robustness in mobile oscillator populations, with implications for resilient biological and engineered collectives. >>

Sayantan Nag Chowdhury, Srilena Kundu. How Mobile Oscillators Reshape Dynamical Robustness in Complex Networks. arXiv: 2610.16608v1 [nlin.AO]. Oct 12, 2026.

https://arxiv.org/abs/2610.16608

Also: network, random, walks, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, randomness, walks, collapse, mobile oscillators, mobility, transition thresholds.

# gst: rich behaviors from stochastic walking with variable long jumps.

AA << propose a generalized model where the random walker takes stochastic jumps of lengths proportional to its present position with certain probability, otherwise it makes forward and backward jumps of fixed (unit) length with given rates. The model exhibits a rich stochastic dynamic behavior.  (AA) obtain exact analytic results for the first two moments of the walker's displacement and show that a phase transition from a diffusive to superdiffusive regime occurs if the stochastic jumps of lengths that are twice (or more) of its present positions are allowed. This phase transition is accompanied by a reentrant diffusive behavior. >> 

Upendra Harbola. Stochastic walker with variable long jumps. Phys. Rev. E 108, 014135. July 28, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.014135 

Also: walk, noise, fluctuations, dance,  in: https://www.inkgmr.net/kwrds.html

Keywords: gst, walks, random walks, noise, fluctuations

# gst: labyrinth chaos: revisiting the elegant, chaotic and hyperchaotic walks

<< Labyrinth chaos was discovered by Otto Rossler and Rene' Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, (AA) celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. >>

 << As all Rossler’s pioneering contributions, labyrinth chaos still holds promise for very interesting further developments. Its simplicity and elegance, both in terms of symmetries, topology and feedback-circuit structure, makes it a good candidate to compare it with other nonlinear, cyclically coupled systems, such as the Arabesques, the Lotka-Voltera system and its variants, and the Arnold-Beltrami-Childress  model. >> 

Vasileios Basios, Chris G. Antonopoulos, Anouchah Latifi. Labyrinth chaos: Revisiting the elegant, chaotic and hyperchaotic walks. arXiv: 2011.11009v1. Nov 22, 2020.

https://arxiv.org/abs/2011.11009