![]() To illustrate aliasing, the Lotka-Volterra model oscillatory regime is numerically sampled, creating prey-predator cycles. ![]() However, to the best of our knowledge, aliasing has never been addressed in the population dynamics context or in coupled oscillatory systems. This effect, known as aliasing, is well described in other areas, such as signal processing and computer graphics. Here, we argue that data regarding population dynamics are prone to misinterpretation when sampling is conducted at a slow rate compared to the population cycle period. These cycles are understood as emerging from the interaction between two or more coupled species. This may be regarded as a theoretical explanation of the existence of flush-pursuer birds, those who uses highly specialized hunting strategy and cross-adapts to the ecosystem relative to the ordinary bird species.Ĭycles in population dynamics are widely found in nature. As an application, it is explained that a predator specie who feed on relatively small number of preys compared to the other predator species must be selective on the available preys in order for long persistence of the ecosystem. An easy graphical method of analysis of the conditions on parameters ensuring long persistence under coexistence is presented. Moreover, the modified version is applicable to simulate a part of a large ecosystem, not only a closed predator-prey system with four species. Parameters in the model are modified so that each of them has its own biological meaning, enabling more intuitive interpretation of biological conditions to the model. This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. The Matlab command ode45 can be used to solve such systems of differential equations. The populations of the prey and predator will be modeled by two differential equations for the early case and with three differential equations for a later model. Later on, we considered very excited model that dealing with one predator and two preys. Initially, we exercised the mathematical model of one prey and one predator. Models of this type are thus called predator-prey models. We are interesting to consider two species of animals interdependence might arise because one species (the “prey”) serves as a food source for the other species (the “predator”). This work focused on applying biological mathematical model to analyzing predation or competition relationships in the natural environment between predators and preys. Modeling efforts of the dynamics of food chains which are initiated long ago confirm that food chains have very rich dynamics. ![]() Most of the ecological systems have the elements to produce divisions and dynamics behavior, and food chains are ecosystems with familiar structure.
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