Predator and Prey Dynamics

We model an adversarial relationship between animals within an ecosystem. The predator–prey equations are a pair of first-order nonlinear differential equations frequently used to describe the dynamics of biological systems.

Left alone, the Prey population waxes without limit as their food supply and reproductive success remain unhindered.

Left alone, the Predator population wanes without sufficient food to sustain their population.

Together the populations vary periodically. These behaviors do not have a simple expression in terms of the usual trigonometric functions, although they are quite tractable. wikipdedia

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