| Abstract: |
| Most of population models, if not all of them, do not have the extinction dynamics. The Lotka-Volterra ordinary differential equations are such cases and solutions never become zero if they are not initially zero. PDE extensions also have the same property and solutions are always positive everywhere. However, the population often becomes zero locally in space and the survival of a species is a global phenomenon. The spatial pattern of biological organisms reflects its history of extinction and growth and the extinction is a key ingredient of spatial patterns. In this paper Lotka-Volterra equations equipped with extinction dynamics are introduced. We will see beautiful patterns of life generated by the newly added extinction dynamics. |
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