58 research outputs found
Spectral control for ecological stability
A system made up of N interacting species is considered. Self-reaction terms
are assumed of the logistic type. Pairwise interactions take place among
species according to different modalities, thus yielding a complex asymmetric
disordered graph. A mathematical procedure is introduced and tested to
stabilise the ecosystem via an {\it ad hoc} rewiring of the underlying
couplings. The method implements minimal modifications to the spectrum of the
Jacobian matrix which sets the stability of the fixed point and traces these
changes back to species-species interactions. Resilience of the equilibrium
state appear to be favoured by predator-prey interactions
Generating directed networks with prescribed Laplacian spectra
Complex real-world phenomena are often modeled as dynamical systems on
networks. In many cases of interest, the spectrum of the underlying graph
Laplacian sets the system stability and ultimately shapes the matter or
information flow. This motivates devising suitable strategies, with rigorous
mathematical foundation, to generate Laplacian that possess prescribed spectra.
In this paper, we show that a weighted Laplacians can be constructed so as to
exactly realize a desired complex spectrum. The method configures as a non
trivial generalization of existing recipes which assume the spectra to be real.
Applications of the proposed technique to (i) a network of Stuart-Landau
oscillators and (ii) to the Kuramoto model are discussed. Synchronization can
be enforced by assuming a properly engineered, signed and weighted, adjacency
matrix to rule the pattern of pairing interactions
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