The present paper deals with a prey–predator model with prey refuge in proportion to both species, and the independent harvesting of each species. Our study shows that using refuge as control, it can break the limit cycle of the system and reach the required state of equilibrium level. We have established the optimal harvesting policy. The boundedness, feasibility of interior equilibria and bionomic equilibrium have been determined. The main observation is that the coefficient of refuge plays an important role in regulating the dynamics of the present system. Moreover, the variation of the coefficient of refuge changes the system from stable to unstable and vice-versa. Some numerical illustrations are given in order to support our analytical and theoretical findings.
Slug Girasia crocea (Godwin-Austen) is an herbivore, feeds on soft twigs or leaves of plants. The slug G. crocea are active for period of March-November. They use to overcome winter month (December-February) through hibernation. Sometimes they were seen to winter morning. In nature, they have a wide range of food acceptability. The feeding and foraging activities are confined to night ours. In nature, breeding period extends from March to November. The egg laying and other breeding activities are maintained at an equal temperature during the whole active period. In laboratory, they thrived well on Amranthus sp. And Spinacea sp., while temperature. They attained adult at the age of 196 days to 201 days. They lay eggs lay in cluster. The eggs are round in shape and white in colour. Individual slugs on an average, added 9.5mm, 2.5mm and 40mg; 13.5mm, 3.5mm and 40mg; 17mm, 5mm and 50mg; 24mm, 5mm and 60 mg; 35.5mm, 6 mm and 485mg; 52mm,10mm and 1190mg; 65mm, 8.5 and 1114mg; 65mm, 9.5mm and 1117mg and 57mm, 10mm and 1134mg to their body length, body width and body weight respectively at temperature of 26 -31.5 0 C during the study period. On an average an egg was measured 3.85mm in diameter.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.