Figure 10.

Neighbouring cells oscillating in anti-phase (standing waves). (a) The power spectrum of fluctuations $P_k^{(\hspace{0.17em}p)h}(\omega )$ and the corresponding phase lag between cells at peak frequency ${\varphi }_{\hspace{0.17em}j,\hspace{0.17em}{j}^{\prime }}^{(\hspace{0.17em}p)h}({\omega }_{\hspace{0.17em}\max })$ as a function of separation (inset). Neighbouring cells tend to oscillate in anti-phase with one another, as demonstrated by the phase lag (inset) and also by the location of the peak of the power spectrum at k = π and non-zero ω. (b) An example of noise-induced standing waves seen in simulations of the stochastic individual-based model. The peaks in one cell tend to align with the troughs in the neighbouring cell, giving rise to chequerboard-type patterns in the figure. The coupling between cells is symmetric (d⁽⁺⁾ = d⁽⁻⁾ = 1). The remaining system parameters are the same as in figure 2 with the exception that $r_h^h=0.07$, $r_{hd}^h=0.93$, τ^(m)h = 20 in all cells and τ^(m)d = 20. (Online version in colour.)