Labyrinth chaos: Revisiting the elegant, chaotic, and hyperchaotic walks

Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we 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. We discuss the properties of the single labyrinth walks system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, what amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walks system by showing that even though it is volume-preserving, it is not force-conservative

A generic model for pandemics in networks of communities and the role of vaccination

The slogan “nobody is safe until everybody is safe” is a dictum to raise awareness that in an interconnected world, pandemics such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible- vaccinated-infected-recovered model with unvaccinated (“Bronze”), moderately vaccinated (“Silver”) and very well vaccinated (“Gold”) communities, connected through different types of networks via a diffusive linear coupling for local spreading. We show that when considering interactions in “Bronze”-“Gold” and “Bronze”-“Silver” communities, the “Bronze” community is driving an increase in infections in the “Silver” and “Gold” communities. This shows a detrimental, unidirectional effect of non-vaccinated to vaccinated communities. Regarding the interactions between “Gold”, “Silver” and “Bronze” communities in a network, we find that two factors play central role: the coupling strength in the dynamics and network density. When considering the spread of a virus in Barabási-Albert networks, infections in “Silver” and “Gold” communities are lower than in “Bronze” communities. We find that the “Gold” communities are the best in keeping their infection levels low. However, a small number of “Bronze” communities are enough to give rise to an increase in infections in moderately and well-vaccinated communities. When studying the spread of a virus in a dense Erdo ̋s-Rényi, and sparse Watts-Strogatz and Barabási-Albert networks, the communities reach the disease-free state in the dense Erdo ̋s-Rényi networks, but not in the sparse Watts-Strogatz and Barabási-Albert networks. However, we also find that if all these networks are dense enough, all types of communities reach the disease- free state. We conclude that the presence of a few unvaccinated or partially vaccinated communities in a network, can increase significantly the rate of infected population in other communities. This reveals the necessity of a global effort to facilitate access to vaccines for all communities

Serre-Green-Naghdi Dynamics under the Action of the Jeffreys’ Wind-Wave Interaction

We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in the context of nonlinear dynamics of surface water waves under wind forcing, in finite depth. The anti-dissipation occurs du to the continuos transfer of wind energy to water surface wave. We find the solitary wave solution of the system, with an increasing amplitude under the wind action. This leads to the blow-up of surface wave in finite time for infinitely large asymptotic space. This dispersive, anti-dissipative and fully nonlinear phenomenon is equivalent to the linear instability at infinite time. The theoretical blow-up time is calculated based on real experimental data. Naturally, the wave breaking takes place before the blow-up time. However, the amplitude’s growth resulting in the blow-up could be observed. Our results show that, based on the particular type of wind-wave tank data used in this paper, for h=0.14m, the amplitude growth rate is of order 0.1 which experimentally, is at the measurability limit. But we think that by gradually increasing the wind speed U10, up to 10 m/s, it is possible to have the experimental confirmation of the present theory in existing experimental facilities