50 citations · 193 across the 18 of their papers we have counts for
18 papers
The disordered logistic map
Joseph W. Baron, Tobias Galla
The logistic map is a quintessential model in the study of low-dimensional chaos. High-dimensional chaos, on the other hand, presents itself in disordered systems with many interac…
Generalised correlations in disordered dynamical systems: Insights from the many-species Lotka-Volterra model
Sebastian Holtedahl Castedo, Joshua Holmes, Joseph William Baron +1
In the study of disordered systems, one often chooses a matrix of independent identically distributed interaction coefficients to represent the quenched random couplings between co…
Interaction networks in persistent Lotka-Volterra communities
Lyle Poley, Tobias Galla, Joseph W. Baron
A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we…
Eigenvalue spectra of finely structured random matrices
Lyle Poley, Tobias Galla, Joseph W. Baron
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As…
A path integral approach to sparse non-Hermitian random matrices
Joseph W. Baron
The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable re…
Analytical and numerical treatment of continuous ageing in the voter model
Joseph W. Baron, Antonio F. Peralta, Tobias Galla +1
The conventional voter model is modified so that an agent's switching rate depends on the `age' of the agent, that is, the time since the agent last switched opinion. In contrast t…
Generalised Lotka-Volterra model with hierarchical interactions
Lyle Poley, Joseph W. Baron, Tobias Galla
In the analysis of complex ecosystems it is common to use random interaction coefficients, often assumed to be such that all species are statistically equivalent. In this work we r…
Eigenvalue spectra and stability of directed complex networks
Joseph W. Baron
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting compone…
Breakdown of random-matrix universality in persistent Lotka--Volterra communities
Joseph W. Baron, Thomas Jun Jewell, Christopher Ryder +1
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The v…
Sampling rare trajectories using stochastic bridges
Javier Aguilar, Joseph W. Baron, Tobias Galla +1
The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemb…
Eigenvalues of random matrices with generalised correlations: a path integral approach
Joseph W. Baron, Thomas Jun Jewell, Christopher Ryder +1
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what fa…
Consensus, polarisation and coexistence in a continuous opinion dynamics model with quenched disorder
Joseph William Baron
A general model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by eve…
Persistent individual bias in a voter model with quenched disorder
Joseph W. Baron
Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure importa…
Dispersal-induced instability in complex ecosystems
Joseph W. Baron, Tobias Galla
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduc…
Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronised oscillations in the presomitic mesoderm
Joseph W. Baron, Tobias Galla
Using a stochastic individual-based modelling approach, we examine the role that Delta-Notch signalling plays in the regulation of a robust and reliable somite segmentation clock.…
Stochastic fluctuations and quasi-pattern formation in reaction-diffusion systems with anomalous transport
Joseph W. Baron, Tobias Galla
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Sta…
Effective diffusion coefficients in reaction-diffusion systems with anomalous transport
Joseph W. Baron, Tobias Galla
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Tu…
Sojourn times and fixation dynamics in multi-player games with fluctuating environments
Joseph W. Baron, Tobias Galla
We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the e…