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Salih Djilali - One of the best experts on this subject based on the ideXlab platform.

  • mathematical analysis of a diffusive predator prey model with herd behavior and prey escaping
    Mathematical Modelling of Natural Phenomena, 2020
    Co-Authors: Fethi Souna, Salih Djilali, Fayssal Charif
    Abstract:

    In this paper, we consider a new approach of prey escaping from herd in a predator-prey model with the presence of Spatial Diffusion. First, the sensitivity of the equilibrium state density with respect to the escaping rate has been studied. Then, the analysis of the non diffusive system was investigated where boundedness, local, global stability, Hopf bifurcation are obtained. Besides, for the diffusive system, we proved the occurrence of Hopf bifurcation and the non existence of Diffusion driven instability. Furthermore, the direction of Hopf bifurcation has been proved using the normal form on the center manifold. Some numerical simulations have been used to illustrate the obtained results.

  • Spatiotemporal Patterns in a Diffusive Predator-Prey Model with Prey Social Behavior
    Acta Applicandae Mathematicae, 2019
    Co-Authors: Salih Djilali, Soufiane Bentout
    Abstract:

    Our aim in this paper is to investigate the behavior of pattern formation for a predator-prey model with social behavior and Spatial Diffusion. Firstly, we give some solution behavior where the non-existence of a non-constant steady state solution has been proved for some values of the Diffusion coefficients. On the other hand, by using the Leray-Schauder degree theory the existence of the non-constant steady-state solution has been proved under a suitable conditions on the Diffusion coefficients.

  • herd behavior in a predator prey model with Spatial Diffusion bifurcation analysis and turing instability
    Journal of Applied Mathematics and Computing, 2018
    Co-Authors: Salih Djilali
    Abstract:

    We consider in this paper an ecological model, in a predator–prey interaction with the presence of a herd behavior. For the analysis of the model, the existence of positive solution and also the existence Hopf bifurcation, Turing driven instability, and Turing–Hopf bifurcation point have bee proved. Then by calculating the normal form, on the center of the manifold associated to the Hopf bifurcation points, the stability of the periodic solution has been proved. In the last part of the paper, numerical simulations has been given to illustrate our theoretical analysis.

R Schlickeiser - One of the best experts on this subject based on the ideXlab platform.

  • modification of the parallel scattering mean free path of cosmic rays in the presence of adiabatic focusing
    The Astrophysical Journal, 2014
    Co-Authors: R Schlickeiser
    Abstract:

    The cosmic ray mean free path in a large-scale nonuniform guide magnetic field with superposed magnetostatic turbulence is calculated to clarify some conflicting results in the literature. A new, exact integro-differential equation for the cosmic-ray anisotropy is derived from the Fokker-Planck transport equation. A perturbation analysis of this integro-differential equation leads to an analytical expression for the cosmic ray anisotropy and the focused transport equation for the isotropic part of the cosmic ray distribution function. The derived parallel Spatial Diffusion coefficient and the associated cosmic ray mean free path include the effect of adiabatic focusing and reduce to the standard forms in the limit of a uniform guide magnetic field. For the illustrative case of isotropic pitch angle scattering, the derived mean free path agrees with the earlier expressions of Beeck & Wibberenz, Bieber & Burger, Kota, and Litvinenko, but disagrees with the result of Shalchi. The disagreement with the expression of Shalchi is particularly strong in the limit of strong adiabatic focusing.

  • a new cosmic ray transport theory in partially turbulent space plasmas extending the quasilinear approach
    The Astrophysical Journal, 2011
    Co-Authors: R Schlickeiser
    Abstract:

    A new transport theory of cosmic rays in magnetized space plasmas with axisymmetric incompressible magnetic turbulence is developed extending the quasilinear approximation to the particle orbit. Arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field are allowed. For quasi-stationary and Spatially homogeneous magnetic turbulence, we derive the small Larmor radius approximation gyrophase-averaged cosmic ray Fokker-Planck coefficients. The generalized Fokker-Planck coefficients correctly reduce to their known quasilinear values in the corresponding limit. New forms of the quasilinear Fokker-Planck coefficients in axisymmetric turbulence are derived which no longer involve infinite sums of products of Bessel functions, which facilitate their numerical computation for specified turbulence field correlation tensors. The Fokker-Planck coefficients for arbitrary phase orbits of the cosmic ray particles provide strict upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients, which in turn yield strict upper and lower limits for the perpendicular and parallel Spatial Diffusion coefficients, respectively, describing the Spatial Diffusion of the isotropic part of the cosmic ray phase space density. For the associated mean free paths, we find for this general case that the product of the minimum parallel mean free path with the sum of the maximum perpendicular mean free paths equals R 2 L , where RL denotes the cosmic ray gyroradius.

J R Jokipii - One of the best experts on this subject based on the ideXlab platform.

  • the longitudinal transport of energetic ions from impulsive solar flares in interplanetary space
    The Astrophysical Journal, 2012
    Co-Authors: J Giacalone, J R Jokipii
    Abstract:

    We present a study of the longitudinal spread of energetic charged particles from a localized instantaneous compact source on the Sun. Our study utilizes a diffusive-transport model for the propagation of energetic ions in interplanetary space. We show that even for very small values of the ratio of perpendicular to parallel Diffusion coefficients—a few percent—the particles spread significantly in longitude. Spatial Diffusion and adiabatic energy loss of ions in the interplanetary plasma cause impulsive particle events at Earth's orbit to last a few days. In this time, the combination of transport both along and across the local Parker-spiral magnetic field and the longitudinal motion of the magnetic lines of forces rooted at the Sun as it rotates leads to substantial longitudinal transport of the particles. We show that spacecraft separated by as much as 180° or more may observe events associated with compact solar sources, such as those from impulsive solar flares. Our results are qualitatively consistent with recent multi-spacecraft observations.

  • velocity correlation and the Spatial Diffusion coefficients of cosmic rays compound Diffusion
    The Astrophysical Journal, 2000
    Co-Authors: J Kota, J R Jokipii
    Abstract:

    We consider the transport of charged particles in a stochastic magnetic field using a method based on the velocity correlation function vi(0)vj(t) developed by R. Kubo. This can be used under very general conditions to evaluate the corresponding Spatial Diffusion coefficients, if the fluctuations are statistically homogeneous in space and time. Although Kubo's theory is quite general, it is not obvious how it can be applied to describe compound Diffusion when particles are strictly tied to the magnetic field lines and perpendicular transport results solely from the random walk of the field lines. This motion is non-Markovian and leads to a slower Δx2 ∝ t1/2 Diffusion in contrast to the Δx2 ∝ t dependence of the standard Diffusion. We demonstrate how compound Diffusion fits into Kubo's formalism. As intuitively as can be anticipated, the non-Markovian nature of the motion results in a long-term anticorrelation in vj(0)vi(t), which causes the ordinary Spatial Diffusion coefficient to vanish identically. The Δx2 ∝ t1/2 dependence of the compound Diffusion can also be recovered from the Laplace transform of the velocity correlation function. Some implications of the long-term anticorrelation are discussed.

Bidhan Chandra Bag - One of the best experts on this subject based on the ideXlab platform.

  • kramers turnover phenomenon in the Spatial Diffusion region
    Journal of Statistical Mechanics: Theory and Experiment, 2016
    Co-Authors: Shrabani Mondal, Bikash C Gupta, Bidhan Chandra Bag
    Abstract:

    In this paper we have presented the dynamics of a Brownian particle with time-delayed feedback. It clearly suggests that the delayed feedback may introduce a dissipation-like effect. As a result of this a breakdown of the fluctuation–dissipation relation occurs and the system behaves like an open one. Therefore, the stationary distribution deviates from the Boltzmann type. It depends on the damping strength. The probability at the barrier top increases with the enhancement of the damping strength. This is a sharp contrast to closed systems (which obey the fluctuation–dissipation relation) and the usual open systems, where the noise strength does not depend on the damping strength. This special feature motivated us to calculate Kramers' rate in the presence of the delayed feedback. Our calculation shows that the activation energy decreases with an increase in the damping strength. This peculiarity introduces a noticeable observation. Kramers' turnover behaviour appears even in the Spatial diffusive regime. Thus its origin is quite different from the known Kramers' turnover, which is a result of an interplay of energy and Spatial diffusive regimes. It should be mentioned here that all our theoretical results are well justified by the numerical experiments.

Yi Zhang - One of the best experts on this subject based on the ideXlab platform.

  • travelling waves of a delayed sir epidemic model with nonlinear incidence rate and Spatial Diffusion
    PLOS ONE, 2011
    Co-Authors: Jing Yang, Siyang Liang, Yi Zhang
    Abstract:

    This paper is concerned with the existence of travlelling waves to a SIR epidemic model with nonlinear incidence rate, Spatial Diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results.