`SNinteraction-2025`

This repository contains interactive versions of figures and computational scripts to reproduce the results shown in figures of

P. Ashwin, C. Postlethwaite, J. Sieber (2026), Local interaction of two systems with saddle-node bifurcations: mutualistic and mixed cases.

Interactive figures

(require javascript)

Figure2.html
Figure5.html
Figure2-Hopf-L1.html (not in the paper, shows Lyapunov coefficient $L_1$ along Hopf bifurcation)

sniceroclinic-coco: scripts for reproducing graphs in Figure 2, Figure 5, and check of criticality of Hopf bifurcation.
sniceroclinic-coco/coco_r3316: snapshot of coco used for the runs. For newest stable version: sourceforge.net/projects/cocotools
MATLAB Code to generate escape time and departure angle figures 6 and 7. Note that plots are created for all labelled points in figures 1 and 2; only a subset of the points from figure 2 are used in figure 7 in the paper.

Computations require Matlab

Enter folder sniceroclinic-coco.
Execute script run_hill_js.m to perform all computations, before continuation of homclinic orbit is possible. Results will be stored in subfolder data.
Execute run_hom.m. This tracks a large-period periodic orbit in two parameters. The branch spends a long time near rthe SNICeroclinic. Along the branch in the bifurcation diagram an approximate location of the saddle-node and of the saddle gets recorded.
Execute script run_homsnic.m, which tracks the SNICeroclinic in 3 parameters mu, gamma, beta. Results will be stored in subfolder data/homsnic (run is called homsnic).
Execute script run_ncsnic.m to obtain bifurcation curve for non-central SNIC in 3 parameters mu, gamma, beta. Results will be stored in subfolder data/ncsnic (run is called ncsnic).
Execute script run_TB_GH.m to obtain bifurcation curves for Takens-Bogdanov and Bautin points in 3 parameters mu, gamma, beta. Results will be stored in subfolders data/hill_btp_run and data/hill_gh_run.
Execute script animate_hom.m to view animation of time profiles of large-period periodic orbits.
Execute script plot_2dbif_mu_gamma.m to generate plots for Figure 2 and Figure2-Hopf-L1.
Execute script plot_3dbif_mu_gamma_beta.m to generate plots for Figure 5.
Execute script hopf_criticality.m to determine formula for Lyapunov coeffficient of Hopf bifurcation.

Run script hilltop_scan_v11.m to generate the figures.

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