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Since the aquatic organisms are very sensitive to the increasing copper contamination in water, this paper focuses on investigating the effects of copper contamination on the interaction between phytoplankton and zooplankton species within both deterministic and stochastic environments. We first construct a deterministic phytoplankton-zooplankton interaction model coupled with the copper concentration and analyze its dynamics, including existence and stability of equilibria, as well as the existence of Hopf bifurcation. A new stochastic model is derived in the form of continuous-time Markov chain (CTMC), and branching process theory is applied to the CTMC model to estimate the extinction probability of zooplankton species. Analytical and numerical findings show that the destiny of species is closely related to the copper concentration, and the predictions of the deterministic and stochastic models may be different in some cases.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.812}, url = {http://global-sci.org/intro/article_detail/jnma/23364.html} }Since the aquatic organisms are very sensitive to the increasing copper contamination in water, this paper focuses on investigating the effects of copper contamination on the interaction between phytoplankton and zooplankton species within both deterministic and stochastic environments. We first construct a deterministic phytoplankton-zooplankton interaction model coupled with the copper concentration and analyze its dynamics, including existence and stability of equilibria, as well as the existence of Hopf bifurcation. A new stochastic model is derived in the form of continuous-time Markov chain (CTMC), and branching process theory is applied to the CTMC model to estimate the extinction probability of zooplankton species. Analytical and numerical findings show that the destiny of species is closely related to the copper concentration, and the predictions of the deterministic and stochastic models may be different in some cases.