189 citations · 267 across the 7 of their papers we have counts for
7 papers
Suppressing escape events in maps of the unit interval with demographic noise
César Parra-Rojas, Joseph D. Challenger, Duccio Fanelli +1
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the m…
Turing instabilities from a limit cycle
Joseph D. Challenger, Raffaella Burioni, Duccio Fanelli
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become un…
Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos
César Parra-Rojas, Joseph D. Challenger, Duccio Fanelli +1
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting…
Topology-driven instabilities: the theory of pattern formation on directed networks
Malbor Asllani, Joseph D. Challenger, Francesco Saverio Pavone +2
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system…
The theory of individual based discrete-time processes
Joseph D. Challenger, Duccio Fanelli, Alan J. McKane
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in…
Intrinsic noise and discrete-time processes
Joseph D. Challenger, Duccio Fanelli, Alan J. McKane
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore i…
Synchronisation of stochastic oscillators in biochemical systems
Joseph D. Challenger, Alan J. McKane
A formalism is developed which describes the extent to which stochastic oscillations in biochemical models are synchronised. It is based on the calculation of the complex coherence…