In this paper, a discrete- time ratio-dependent prey- predator model is proposed and analyzed. All possible fixed points have been obtained. The local stability conditions for these fixed points have been established. The global stability of the proposed system is investigated numerically. Bifurcation diagrams as a function of growth rate of the prey species are drawn. It is observed that the proposed system has rich dynamics including chaos.

The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

This study evaluated the functional response of the larva of the predator Chrysoperla carnea by offering varying densities of cabbage aphid, Brevicoryne brassicae (L.) . Results showed conformity with type–II functional response, where the number of prey killed approaches asymptote hyperbolically as prey density increases (declining proportion of prey killed or the inverse density dependent) till it reached the stability stage determined by handling time and predator satiation. Also, the values of attack rate and handling time changed with age progress for both predator and prey. It has been observed an increase in the attack rate and reduction in handling time with the progress of the predator age when feeding on a particular nymphal in

The study of Mars's ionosphere was made by investigating the measurements of the electron density (Ne) depending of the variation of the solar activities through different local time, different seasons, and different altitudes. The datasets has been taken from MARSIS on board the Mars Express spacecraft, the investigation for the solar indices and the electron density (Ne) have been made for two period of time depending on the strength of the geomagnetic storms, the first one was taken when the geomagnetic storms was low as in years (1998 & 2005), the data was chosen for three seasons of these years, Winter (December), Summer (June) and Spring (April). The second period was taken for the years (2001 & 2002) when the geomagnetic s

The study of Mars's ionosphere was made by investigating the measurements of the electron density (Ne) depending of the variation of the solar activities through different local time, different seasons, and different altitudes. The datasets has been taken from MARSIS on board the Mars Express spacecraft, the investigation for the solar indices and the electron density (Ne) have been made for two period of time depending on the strength of the geomagnetic storms, the first one was taken when the geomagnetic storms was low as in years (1998 & 2005), the data was chosen for three seasons of these years, Winter (December), Summer (June) and Spring (April). The second period was taken for the years (2001 & 2002) when the geomagnetic s

Results of exposure larvae of the most important predator in the integrated pest management , the green lacewings, Chrysoperla carnea (Stephens) to various densities of fig moth Ephestia cautella eggs showed increasing in the number of consumed prey at decreasing rate of increasing prey density where curve slope consumption decreased gradually until leveling off. These specifications concurred with type II functional response that predators appear towards varied densities of its preys ,that was confirm by logistic regression between the proportion of prey eaten in relation to prey offered . Third larval instars of the predator showed attack rate (a) of 4.85. This was greater than the second larval instar (3.58). Handling time (Th) per

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and und