Non-reciprocal interactions enhance heterogeneity

Abstract

We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links. By assuming the system to exhibit a stable homogeneous equilibrium whenever only local interactions are considered, we prove that such equilibrium can turn unstable once suitable non-reciprocal long-range interactions are allowed for. Stated differently we propose sufficient conditions allowing for patterns to emerge using a non-symmetric coupling, while initial perturbations about the homogenous equilibrium fade away assuming reciprocal coupling. The instability, precursor of the emerging spatio-temporal patterns, can be traced back, via a linear stability analysis, to the complex spectrum of an interaction non-symmetric Laplace operator. Taken together, our results pave the way for the understanding of the many and heterogeneous patterns of complexity found in ecological, chemical or physical systems composed by interacting parts, once no diffusion takes place.

References in corpus (7)

• Synchronization in complex networks
• Turing patterns in network-organized activator-inhibitor systems
• Synchronization is optimal in non-diagonalizable networks
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Turing patterns in multiplex networks
• The role of modularity in self-organisation dynamics in biological networks
• Synchronization dynamics in non-normal networks: the trade-off for optimality

Cited by in corpus (8)

• Synchronization induced by directed higher-order interactions
• Turing patterns in systems with high-order interactions
• Turing patterns on discrete topologies: from networks to higher-order structures
• A generalized Routh-Hurwitz criterion for the stability analysis of polynomials with complex coefficients: application to the PI-control of vibrating structures
• Robustness of travelling states in generic non-reciprocal mixtures
• Pattern reconstruction through generalized eigenvectors on defective networks
• Stabilization of hyperbolic reaction-diffusion systems on directed networks through the generalized Routh-Hurwitz criterion for complex polynomials
• Nonreciprocity induced spatiotemporal chaos: Reactive vs dissipative routes