We propose a novel generic information-theoretic framework for characterizing the task difficulty in the Collective Perception paradigm. Our formalism builds on the notion of Empowerment - a task-independent, universal and generic utility function, which characterizes the level of perceivable control an embodied agent has over its environment. Series of simulations with an empowerment model of the collective perception scenario revealed a significant correlation between the levels of empowerment and the accuracy demonstrated by a set of standard collective decision-making strategies and a recent state-of-the-art neural network controller on nine benchmark patterns, used previously for assessing swarm performance. The results elucidate the key role of both the agent embodiment and the environmental pattern in characterising task difficulty, and justify the application of empowerment to analytically assess this role, which could help predict swarm performance and support the development of more efficient decision-making strategies.

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. Understanding the topological features of the networks that affect the resilience phenomenon remains a challenging goal for the design of robust complex systems. We hereby introduce the concept of non-normal networks, namely networks whose adjacency matrices are non-normal and we show that such feature can drastically change the global dynamics through an amplification of the system response to exogenous disturbances and eventually impact the system resilience. This early stage transient period can induce the formation of inhomogeneous patterns, even in systems involving a single diffusing agent, providing thus a new kind of dynamical instabilities complementary to the Turing one. We provide an illustrative application of this result to ecology by proposing a mechanism to mute the Allee effect.