Hopf Point Analysis for Ratio-Dependent Food Chain Models

Ratio-Dependent Food Chain Models with Three Trophic Levels

In this paper we study a food chain model with three trophic levels and Michaelis-Menten type ratio-dependent functional response. Distinctive feature of this model is the sensitive dependence of the dynamical behavior on the initial populations and parameters of the real world. The stability of the equilibrium points are also investigated. Keywords—Food chain, Ratio dependent models, Three lev...

Hopf Point Analysis for Angiogenesis Models

In this paper we present several ODE systems encoding the most essential observations and assumptions about the complex hierarchical interactive processes of tumor neo-vascularization (angiogenesis). From experimental results we infer that a significant marker of tumor aggressiveness is the oscillatory behavior of tumor size, which is driven by its vascularization dynamics. To study the forces ...

analysis of ruin probability for insurance companies using markov chain

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Bifurcation analysis and control of chaos for a hybrid ratio-dependent three species food chain

Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model

In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coex...