In ecology, the food chain pyramid suggests that there must be less consumersrnthan their food source. In our case the balance in the population of plants andrnherbivores should be maintained in the ecosystem. Otherwise, the extinction of onernor both population may occur. In the interaction between plants and herbivoresrnthat live in the same ecosystem, understanding the conditions in which coexistencernequilibrium occurs answers a major question in ecology. In this interaction, plantsrnserve as food for herbivores. Then the livelihood of herbivores highly depend onrnthe availability of plants. Moreover, the abundance of the plant density alone doesrnnot guarantee the non-extinction of the herbivore population as they are assumedrnto reproduce sexually. Plant-herbivore relationship depends also on environmentalrnfactors like rainfall, temperature and altitude. Due to global climate change thernincrease/decrease in temperature and also in rainfall will have an effect on theirrninteraction. Environmental noises both positive (such as putting extra water sourcernfor the herbivores, or fencing the land to recover by keeping herbivores away) andrnnegative (such as animal/plant disease) often affect population dynamics.rnIn this study, threshold conditions are obtained for the non extinction of the herbivorernpopulation and a trapping region is obtained to ensure coexistence of the population.rnMoreover, it has been shown that the dynamics of the population is significantlyrnsensitive to the feeding rate and the harvest rate of the herbivore population. Itrnwas also found that the environmental noises added to the herbivore populationrnresulted more change in the dynamics than those added to the plant populationrn(food source). Ignoring the environmental noise could make the land managementrnand wild life conservation difficult to maintain their goals.rnFurthermore, considering periodically changing rainfall and temperature, it has beenrnshown that we can find a trapping region for the coexistence of populations. Tornvalidate the results of the mathematical model, real data from the Genale-Dawarnriver basin in the southern part of Ethiopia, is collected and used. The river basinrnrepresents the three major climatic zones of the country, the cool zone, temperaternzone and hot lowlands. It is also found that if the temperature and rainfall variesrnwith in 10% there is a possibility of extinction of population. This needs the attentionrnof an environmental conservation people and/or those people who are animalrnfarmers.