Spatiotemporal pattern selection in a nontoxic-phytoplankton - toxic-phytoplankton - zooplankton model with toxin avoidance effects

• Published in: Applied mathematics and computation 2022-06, Vol.423, p.127007, Article 127007
• Main Authors: Zhang, Feifan, Sun, Jiamin, Tian, Wang
• Format: Article
• Language: English
• Subjects: Amplitude equation; Cross-diffusion; Pattern formation; Toxin avoidance
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127007

•Toxin avoidance effects are considered in space as a cross-diffusion term in a nontoxic-phytoplankton - toxic phytoplankton - zooplankton model.•Amplitude analysis on the three species system are explored; Stripes, hexagons, and mixed patterns of stripes can be expected through the theoretical analysis.•As toxin avoidance effects increase (cross-diffusion coefficient), system goes through different stages of pattern selection.•Numerical simulations are consistent with the results of theoretical analysis. In this research, considering the toxin avoidance effects of zooplankton to toxic phytoplankton in space as cross-diffusion terms, a modified model is proposed on the complex spatiotemporal dynamics of non-toxic phytoplankton, toxic phytoplankton and zooplankton system. In order to explore the toxin avoidance effects on pattern formation and selection, Turing bifurcation analysis and amplitude analysis are performed. The results of Turing analysis show that patterns can be formed when diffusion coefficient is less than a critical value. Amplitude equations are calculated and amplitude analysis show that stripe patterns, hexagon patterns and mixed patterns of stripes and hexagons can be theoretically predicted. Focusing on toxin avoidance coefficient (cross-diffusion coefficient) and diffusion coefficient of zooplankton, parameter space for pattern formation and selection is plotted. Numerical simulations on pattern formation are carried out to validate the theoretical analysis with five groups of parameters. With the increase of toxin avoidance effects, simulated patterns can be obtained as hexagons, mixed patterns of stripes and hexagons, stripes, mixed patterns of stripes and hexagons, and hexagons. Finally, taking stripe pattern as an example, simulated pattern is compared with predicted pattern. Simulation results are all consistent with theoretical analysis.