Sentence examples for minimal wave speed from inspiring English sources

This paper is concerned with the minimal wave speed in a nonlocal dispersal predator prey system with delays.

Remark 4.2 By what we have done, c ∗ is the minimal wave speed of monotone traveling wave solutions of (1.1).

Many investigators considered its traveling wave solutions connecting different spatial homogeneous steady states such as the existence, monotonicity, minimal wave speed and stability; see [1 16].

A corresponding space-time plot is given in Figure 5b, which illustrates that the speed of the front asymptotically approaches the calculated minimal wave speed c0.

In this section, we confirm that c ∗ is the minimal wave speed of monotone invasion traveling wave solutions by presenting the following nonexistence of monotone traveling wave solutions.

By presenting the existence and nonexistence of traveling wave solutions, we confirm that the threshold is the minimal wave speed, which completes the known results.

Linearising ahead of the wave, the p-equation decouples and a travelling wave analysis indicates that there is a minimum wave speed which is independent of δ.

Under appropriate assumptions, we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions.

Recently, Pan [43] estimated the invasion speed of the predator in a predator prey system, which equals the minimal invasion wave speed in Lin [44].

By introducing the definition of asymptotic spreading speed to describe the spreading front, we provide an estimate to show that the boundary moving speed cannot be faster than the minimal traveling wave speed.

To investigate the consequences for wave speed all that would be required would be a minimal extension of the formula for interface dynamics (13) with the replacement of the numerator (u_{t}) according to (u_{t} rightarrow u_{t} - h_{t}).