Dynamics induced by delay in a nutrient–phytoplankton model with diffusion

Stability and bifurcation analysis of a nutrient‐phytoplankton model with time delay

“…[6][7][8][9][10][11][12] Models also provide quantitative insights into phytoplankton growth by exploring the complex intraspecific and interspecific interactions that typically involve phytoplankton populations, as shown by several previous studies on the dynamic mechanisms of phytoplankton blooms. [13][14][15][16][17][18] Most models of phytoplankton growth consist of two or three components including a limiting nutrient, a phytoplankton population, and a zooplankton population, [19][20][21][22][23] and the corresponding analysis focuses on dynamics, [24][25][26][27][28][29][30][31] such as persistence, extinction, stability, and bifurcation. Although these models represent abstractions of real-world phenomena, they are extremely useful to study phytoplankton growth dynamics.…”

Delay driven Hopf bifurcation and chaos in a diffusive toxin producing phytoplankton‐zooplankton model

“…As is well known, spatial diffusion is important for producing more complicated and richer dynamical behaviors . Additionally, a wide variety of plankton systems with diffusion have been proposed and analyzed to understand the role of phytoplankton in harmful algae blooms (HABs) .…”

“…As is well known, spatial diffusion is important for producing more complicated and richer dynamical behaviors. [13][14][15] Additionally, a wide variety of plankton systems with diffusion have been proposed and analyzed to understand the role of phytoplankton in harmful algae blooms (HABs). [16][17][18][19][20] In 2008, S. Roy 18 considered the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water, which showed that spatial movements of planktonic systems in the presence of TPP could generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, and further ensure the persistence of multiple species in space and time.…”

Traveling waves for a reaction-diffusion model with a cyclic structure

“…If γ = 1, δ > σ, f (u) = βu, then system (1) denotes the famous SIS disease model with natural and disease-related death rates incorpotated [16], where u denotes the susceptible and v is the infective. If d 1 = d 2 , f (u) = bu/(a + u), system (1) becomes the diffusive nutrient-phytoplankton model in [5] without time delay, where u stands for nutrients and v is the phytoplankton. However, according to the arguments in [6], the nutrient uptake rate of phytoplankton f (u) can have a general form satisfying assumption (A1).…”