# Control of multidimensional systems on complex network

## TL;DR

This paper introduces a control method for multidimensional systems on complex networks, using a new species as a controller and the root locus method to achieve stable equilibria, demonstrated on synthetic and real data.

## Contribution

It proposes a novel control approach for complex network systems by adding a species as a controller and employing the root locus method for stability shaping.

## Key findings

- Effective control of complex network systems demonstrated
- Robustness shown on synthetic and real data
- Stable equilibria achieved through the proposed method

## Abstract

Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in families, homogeneous in kind. These latter interact selectively, through a sequence of self-consistently regulated steps, whose deeply rooted architecture is stored in the assigned matrix of connections. The asymptotic equilibrium eventually attained by the system, and its associated stability, can be assessed by employing standard nonlinear dynamics tools. For many practical applications, it is however important to externally drive the system towards a desired equilibrium, which is resilient, hence stable, to external perturbations. To this end we here consider a system made up of $N$ interacting populations which evolve according to general rate equations, bearing attributes of universality. One species is added to the pool of interacting families and used as a dynamical controller to induce novel stable equilibria. Use can be made of the root locus method to shape the needed control, in terms of intrinsic reactivity and adopted protocol of injection. The proposed method is tested on both synthetic and real data, thus enabling to demonstrate its robustness and versatility.