3 papers
nlin.SI2026
New Families and Operations on Integrable Graphs
Matthew Visomirski, Christopher Griffin
In this paper, we investigate the integrability of Lotka-Volterra (replicator) systems arising from interaction matrices generated from corresponding graph structures, continuing w…
nlin.PS2026
Coherent Structures and Travelling Waves in Spatial Replicators from a Biased Volterra Lattice
Matthew Visomirski, Christopher Griffin
The Volterra lattice is a well-known integrable family that is also a special class of replicator dynamics and whose members can be put in one-to-one correspondence with the direct…
nlin.SI2024
Integrability of Generalised Skew-Symmetric Replicator Equations via Graph Embeddings
Matthew Visomirski, Christopher Griffin
It is known that there is a one-to-one mapping between oriented directed graphs and zero-sum replicator dynamics (Lotka-Volterra equations) and that furthermore these dynamics are…