3 research outputs found
Non-Gaussian fluctuations in stochastic models with absorbing barriers
The dynamics of a one-dimensional stochastic model is studied in presence of
an absorbing boundary. The distribution of fluctuations is analytically
characterized within the generalized van Kampen expansion, accounting for
higher order corrections beyond the conventional Gaussian approximation. The
theory is shown to successfully capture the non Gaussian traits of the sought
distribution returning an excellent agreement with the simulations, for {\it
all times} and arbitrarily {\it close} to the absorbing barrier. At large
times, a compact analytical solution for the distribution of fluctuations is
also obtained, bridging the gap with previous investigations, within the van
Kampen picture and without resorting to alternative strategies, as elsewhere
hypothesized.Comment: 2 figures, submitted to Phys. Rev. Let
Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions
A stochastic model of autocatalytic chemical reactions is studied both
numerically and analytically. The van Kampen perturbative scheme is
implemented, beyond the second order approximation, so to capture the non
Gaussianity traits as displayed by the simulations. The method is targeted to
the characterization of the third moments of the distribution of fluctuations,
originating from a system of four populations in mutual interaction. The theory
predictions agree well with the simulations, pointing to the validity of the
van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
When does cyclic dominance lead to stable spiral waves?
Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion