In this paper, a spatial predator-prey system with Beddington -
DeAngelis functional response and... more In this paper, a spatial predator-prey system with Beddington - DeAngelis functional response and the modified Leslie - Gower type dynamics under homogeneous Neumann boundary condition is considered. The local and global asymptotic stability of the unique positive homogeneous steady state of the corresponding temporal model are discussed. Moreover, the local stability of the unique constant steady state of the spatiotemporal model is investigated and it is pointed out that spatial patterns cannot occur in the vicinity of this stable steady state.
In this paper a modified Leslie-Gower predator-prey system with Beddington-DeAngelis functional r... more In this paper a modified Leslie-Gower predator-prey system with Beddington-DeAngelis functional response under homogeneous Neumann boundary condition is considered. The prey and predator species are assumed to have equal diffusion coefficient. The possibility of non-Turing spatio-temporal patterns is explored. The ratio of two intrinsic growth rates is considered as a control parameter. Regular spatio-temporal oscillatory patterns as well as non-stationary irregular patterns are obtained. The numerical simulations reveal the dependence of the patterns on the choice of initial distribution and reaction parametric values.
A three species food web comprising of two preys and one predator in an isolated homogeneous habi... more A three species food web comprising of two preys and one predator in an isolated homogeneous habitat is considered. The preys are assumed to grow logistically. The predator follows modified Leslie-Gower dynamics and feeds upon the prey species according to Holling Type II functional response. The local stability of the constant positive steady state of the corresponding temporal system and the spatio-temporal system are discussed. The existence and non-existence of non- constant positive steady states are investigated.
In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type ... more 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 bi-furcation 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 coexistence of spotted and stripe – like patterns.
In this paper, the spatiotemporal dynamics of a modified Leslie-Gower predator-prey system with B... more In this paper, the spatiotemporal dynamics of a modified Leslie-Gower predator-prey system with Beddington -DeAngelis functional response incorporating constant proportion of prey refuge under homogeneous Neumann boundary condition is investigated. The local and global asymptotic stability of the unique positive homogeneous steady state in the absence of diffusion are discussed. Furthermore, we perform a series of numerical simulations and the results of the numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe like or spotted or coexistence of both..
In this paper, a spatial predator-prey system with Beddington -
DeAngelis functional response and... more In this paper, a spatial predator-prey system with Beddington - DeAngelis functional response and the modified Leslie - Gower type dynamics under homogeneous Neumann boundary condition is considered. The local and global asymptotic stability of the unique positive homogeneous steady state of the corresponding temporal model are discussed. Moreover, the local stability of the unique constant steady state of the spatiotemporal model is investigated and it is pointed out that spatial patterns cannot occur in the vicinity of this stable steady state.
In this paper a modified Leslie-Gower predator-prey system with Beddington-DeAngelis functional r... more In this paper a modified Leslie-Gower predator-prey system with Beddington-DeAngelis functional response under homogeneous Neumann boundary condition is considered. The prey and predator species are assumed to have equal diffusion coefficient. The possibility of non-Turing spatio-temporal patterns is explored. The ratio of two intrinsic growth rates is considered as a control parameter. Regular spatio-temporal oscillatory patterns as well as non-stationary irregular patterns are obtained. The numerical simulations reveal the dependence of the patterns on the choice of initial distribution and reaction parametric values.
A three species food web comprising of two preys and one predator in an isolated homogeneous habi... more A three species food web comprising of two preys and one predator in an isolated homogeneous habitat is considered. The preys are assumed to grow logistically. The predator follows modified Leslie-Gower dynamics and feeds upon the prey species according to Holling Type II functional response. The local stability of the constant positive steady state of the corresponding temporal system and the spatio-temporal system are discussed. The existence and non-existence of non- constant positive steady states are investigated.
In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type ... more 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 bi-furcation 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 coexistence of spotted and stripe – like patterns.
In this paper, the spatiotemporal dynamics of a modified Leslie-Gower predator-prey system with B... more In this paper, the spatiotemporal dynamics of a modified Leslie-Gower predator-prey system with Beddington -DeAngelis functional response incorporating constant proportion of prey refuge under homogeneous Neumann boundary condition is investigated. The local and global asymptotic stability of the unique positive homogeneous steady state in the absence of diffusion are discussed. Furthermore, we perform a series of numerical simulations and the results of the numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe like or spotted or coexistence of both..
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Papers by Dawit Melese
DeAngelis functional response and the modified Leslie - Gower type
dynamics under homogeneous Neumann boundary condition is
considered. The local and global asymptotic stability of the unique
positive homogeneous steady state of the corresponding temporal model
are discussed. Moreover, the local stability of the unique constant steady
state of the spatiotemporal model is investigated and it is pointed out that
spatial patterns cannot occur in the vicinity of this stable steady state.
The local stability of the constant positive steady state of the corresponding temporal system and the spatio-temporal system are discussed. The existence and non-existence of non- constant positive steady states are investigated.
DeAngelis functional response and the modified Leslie - Gower type
dynamics under homogeneous Neumann boundary condition is
considered. The local and global asymptotic stability of the unique
positive homogeneous steady state of the corresponding temporal model
are discussed. Moreover, the local stability of the unique constant steady
state of the spatiotemporal model is investigated and it is pointed out that
spatial patterns cannot occur in the vicinity of this stable steady state.
The local stability of the constant positive steady state of the corresponding temporal system and the spatio-temporal system are discussed. The existence and non-existence of non- constant positive steady states are investigated.