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arXiv · 2509.01715

Quadratic Growth Model with Discontinuity: A Link between Monostable and Bistable Traveling Waves

Wonhyung Choi·Junsik Bae·Yong-Jung Kim
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Abstract

We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures finite-time extinction for sub-threshold populations. This discontinuity induces a free boundary in the wave profile, a phenomenon that distinguishes the model from the classical logistic or Allen-Cahn equations. A complete scenario is presented that connects monostable and bistable traveling waves through the wave speed parameter, thereby providing a unified framework for their dynamics.

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Wonhyung Choi, Junsik Bae, Yong-Jung Kim. 2025-09-01. Quadratic Growth Model with Discontinuity: A Link between Monostable and Bistable Traveling Waves. https://arxiv.org/abs/2509.01715

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