Table 3 Classification of travelling wave solutions arising from different classes of PDEs with Allee kinetics.
Diffusivity function classification | Allee effect | Travelling wave | Front type | Direction |
|---|---|---|---|---|
Constant | Weak/Reverse | Yes | Smooth | Positive |
Constant | Strong | Yes | Smooth | Positive |
Constant | Strong | Yes | Smooth | Negative |
Strictly positive | Weak/Reverse | Yes | Smooth | Positive |
Strictly positive | Strong | Yes | Smooth | Positive |
Strictly positive | Strong | Yes | Smooth | Negative |
Extinction-degenerate non-negative | Weak/Reverse | Yes | Sharp | Positive |
Extinction-degenerate non-negative | Strong | Yes | Sharp | Positive |
Extinction-degenerate non-negative | Strong | Yes | Smooth | Negative |
Positive-negative-positive | Weak/Reverse | Yes | Smooth | Positive |
Positive-negative-positive | Strong | Yes | Shock | Positive |
Positive-negative-positive | Strong | Yes | Shock | Negative |
Capacity-degenerate positive-negative | Weak/Reverse | Yes | Smooth | Positive |
Capacity-degenerate positive-negative | Strong | No | N/A | N/A |
Positive-negative | Weak/Reverse | Yes | Smooth | Positive |
Positive-negative | Strong | No | N/A | N/A |
