  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.
