Topological resilience in non-normal networked systems

The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g. cascade failures in computer networks or parasitic species invasion in ecosystems. Understanding the networks topological features that affect the resilience phenomenon remains a challenging goal of the design of robust complex systems. We prove that the non-normality character of the network of interactions amplifies the response of the system to exogenous disturbances and can drastically change the global dynamics. We provide an illustrative application to ecology by proposing a mechanism to mute the Allee effect and eventually a new theory of patterns formation involving a single diffusing species

Topological resilience in non-normal networked systems

The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g. cascade failures in computer networks or parasitic species invasion in ecosystems. Understanding the networks topological features that affect the resilience phenomenon remains a challenging goal of the design of robust complex systems. We prove that the non-normality character of the network of interactions amplifies the response of the system to exogenous disturbances and can drastically change the global dynamics. We provide an illustrative application to ecology by proposing a mechanism to mute the Allee effect and eventually a new theory of patterns formation involving a single diffusing species

Hamiltonian control of Kuramoto oscillators

Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are however cases where synchronisation acts against the stability of the system; for instance in the case of engineered structures, resonances among sub parts can destabilise the whole system. In this Letter we propose an innovative control method to tackle the synchronisation process based on the use of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronisation. We present our results on the paradigmatic Kuramoto model but the applicability domain is far more large

Turing patterns in multiplex networks

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of an homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations

Hopping in the crowd to unveil network topology

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node that can be chosen randomly. The technique is successfully tested against both synthetic and real data, and shown to estimate with great accuracy also the total number of nodes

Pattern formation for reactive species undergoing anisotropic diffusion

Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive. Under this working hypothesis, the conditions for the onset of the instability are mathematically derived and numerically validated. Patterns which closely resemble those obtained in the classical context of isotropic diffusion, develop when the usual Turing condition is violated, along one of the two accessible directions of migration. Remarkably, the instability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched