# Topological resilience in non-normal networked systems

## TL;DR

This paper investigates how the non-normality of network interactions influences the resilience of complex systems, revealing that non-normality amplifies responses to disturbances and affects global dynamics, with applications in ecology.

## Contribution

It demonstrates that non-normal network structures significantly impact system resilience and introduces a new ecological theory related to pattern formation and disturbance response.

## Key findings

- Non-normality amplifies system response to disturbances.
- Non-normal networks can alter global dynamics.
- Application to ecology shows potential to control species invasion.

## Abstract

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.