DYNAMIC ANALYSIS OF A FRACTIONAL ORDER PHYTOPLANKTON MODEL

Mohamad Javidi; Nemat Nyamoradi

doi:10.11948/2013026

2013 Volume 3 Issue 4

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Mohamad Javidi, Nemat Nyamoradi. DYNAMIC ANALYSIS OF A FRACTIONAL ORDER PHYTOPLANKTON MODEL[J]. Journal of Applied Analysis & Computation, 2013, 3(4): 343-355. doi: 10.11948/2013026

Citation:

Mohamad Javidi, Nemat Nyamoradi. DYNAMIC ANALYSIS OF A FRACTIONAL ORDER PHYTOPLANKTON MODEL[J]. Journal of Applied Analysis & Computation, 2013, 3(4): 343-355. doi: 10.11948/2013026

DYNAMIC ANALYSIS OF A FRACTIONAL ORDER PHYTOPLANKTON MODEL

1 Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran;
2 Department of Mathematics, Faculty of Sciences Razi University, 67149 Kermanshah, Iran

Abstract

Abstract

The fractional order phytoplankton model (PM) can be written as d^αP_s/dt^α=rP_s(1 -P_s/K) -υP_sP_i/(P_s+1) + γ₁P_i, d_αP_in/dt^α=υP_sP_i/(P_i+1) -βP_in, d^αP_s/dt^α=β₁P_in -δP_i, P_s(ξ)=ϱ₀, P_i(ξ)=ϱ₁, P_in(ξ)=ϱ₂, where P_s and P_i be the population densities of susceptible and infected phytoplankton respectively and P_in be the population density of population in incubated class. In this paper, stability analysis of the phytoplankton model is studied by using the fractional Routh-Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PM.
- Phytoplankton model /
- Routh-Hurwitz stability conditions /
- numerical simulation
MSC: 26A33;37B55

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References

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