This study analyzed the effect of nonlinear dynamic parameter of phytoplankton toxin emission on the system. Many previous studies have indicated that the zooplankton, mollusks, and habitat factors generate nonlinear chaotic dynamic behavior, which is hardly controlled random behavior. Therefore, in order to understand in what parameter conditions the system has this nonlinear behavior, the linear and nonlinear behaviors resulting from different conditions are discussed. This study used numerical analysis of differential transformation method to analyze the phase of system and applied bifurcation diagrams, trajectory diagrams, Poincaré maps, and spectrograms to discuss and validate whether the system has chaos phenomenon
In this paper, a new mathematical model has been proposed and analyzed to study the interaction of p...
In this paper, a predator–prey model with Allee effect and seasonally forcing in the prey’s growth r...
In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with t...
Abstract. We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-cha...
Toxin producing phytoplankton (TPP) plays an important role in aquatic systems. To observe the role ...
We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-chain mo...
The challenges to live in the open water and the diversity of habitats in the marine environments pr...
A nonlinear system describing the interaction between toxin-producing phytoplankton and zooplankton ...
We investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pai...
Phytoplankton bloom has become a growing global concern in recent years due to the exc...
In this paper, classes of mathematical models of phytoplankton-zooplankton systems with toxic phytop...
Nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developme...
Modeling of ecological processes is demonstrated using a newly developed nonlinear dynamics model of...
Dynamics of aquatic biological communities in patchy environments is a topic of substantial interest...
Abstract The local dynamics with different topological classifications, bifurcation analysis, and ch...
In this paper, a new mathematical model has been proposed and analyzed to study the interaction of p...
In this paper, a predator–prey model with Allee effect and seasonally forcing in the prey’s growth r...
In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with t...
Abstract. We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-cha...
Toxin producing phytoplankton (TPP) plays an important role in aquatic systems. To observe the role ...
We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-chain mo...
The challenges to live in the open water and the diversity of habitats in the marine environments pr...
A nonlinear system describing the interaction between toxin-producing phytoplankton and zooplankton ...
We investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pai...
Phytoplankton bloom has become a growing global concern in recent years due to the exc...
In this paper, classes of mathematical models of phytoplankton-zooplankton systems with toxic phytop...
Nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developme...
Modeling of ecological processes is demonstrated using a newly developed nonlinear dynamics model of...
Dynamics of aquatic biological communities in patchy environments is a topic of substantial interest...
Abstract The local dynamics with different topological classifications, bifurcation analysis, and ch...
In this paper, a new mathematical model has been proposed and analyzed to study the interaction of p...
In this paper, a predator–prey model with Allee effect and seasonally forcing in the prey’s growth r...
In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with t...