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<p>In this paper, we mainly focus on spatial and chaotic behavior in an aquatic ecosystem, three species (fish, zooplankton, and phytoplankton) with Holling type II functional responses with or without diffusion. The analyses of equilibrium, stability, and bifurcation have been produced. It is examined how chaotic events may be produced by the system and how sensitive it is to the half-saturation constant. The maximal Lyapunov exponent calculation and the existence of an odd attractor both demonstrate that the model has chaotic dynamics. We conclude that chaotic dynamics can be influenced by the half-saturation constant. We employ fundamental nonlinear dynamics tools, such as the Poincare section and maximum Lyapunov exponent, to ascertain the system’s chaotic behavior. In the spatial model, we also develop requirements for Turing instability, and we observe several time-step-based Turing patterns, with a focus on the role of diffusion variation. In addition, we were able to collect the spatial system’s time assessment pattern construction, mutual interference, which has both stabilizing and destabilising effects, is another factor that contributes to chaos. According to our research, the harmful substances that the three species (fish, zooplankton, and phytoplankton) population releases may act as a biocontrol by creating order out of chaos.</p>

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A Toxins Role in Controlling Chaos with a Spatial Effect in an Aquatic Systems

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Randhir Singh Baghel

摘要

In this paper, we mainly focus on spatial and chaotic behavior in an aquatic ecosystem, three species (fish, zooplankton, and phytoplankton) with Holling type II functional responses with or without diffusion. The analyses of equilibrium, stability, and bifurcation have been produced. It is examined how chaotic events may be produced by the system and how sensitive it is to the half-saturation constant. The maximal Lyapunov exponent calculation and the existence of an odd attractor both demonstrate that the model has chaotic dynamics. We conclude that chaotic dynamics can be influenced by the half-saturation constant. We employ fundamental nonlinear dynamics tools, such as the Poincare section and maximum Lyapunov exponent, to ascertain the system’s chaotic behavior. In the spatial model, we also develop requirements for Turing instability, and we observe several time-step-based Turing patterns, with a focus on the role of diffusion variation. In addition, we were able to collect the spatial system’s time assessment pattern construction, mutual interference, which has both stabilizing and destabilising effects, is another factor that contributes to chaos. According to our research, the harmful substances that the three species (fish, zooplankton, and phytoplankton) population releases may act as a biocontrol by creating order out of chaos.