The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect

Figure 1.  The image of an integral kernel $ K $ with the Mexican hat profile on $ {\mathbb{R}} $

Figure 2.  The images of localized patterns. (a) Pulse solution when $ P^{+} = P^{-} = \mathit{\boldsymbol{0}} $. (b) Front solution when $ n = 1 $ and $ P^{+}>P^{-} $

Figure 3.  The image of $ P(z;\mathit{\boldsymbol{h}}) $ when $ N = 2 $

Figure 4.  The image of $ P(z;\mathit{\boldsymbol{h}}) $. (a) $ (N^+, N^-) = (1,1) $. (b) $ (N^+, N^-) = (2,1) $

Figure 5.  The image of the interaction of two standing fronts, when the kernel is a non-negative function

Figure 6.  (a) The graph of (30) when $ \varepsilon = 0.01,\ q_1 = 1.0,\ q_2 = 2.0 $. (b) The graph of $ G(\lambda) $ when $ d = 1.0 $, $ f'(1) = -1 $ and the integral kernel is same as Figure 6 (a)

Figure 7.  (a) The numerical solution of $ (2) $ on the interval $ (0,40) $ when $ t = 100.0 $, where $ f(u) = \frac{1}{2}u(1-u^2) $ and the other parameters are same as that in >Figure 6. (b) The graph of $ \log|u(t,x)-1| $ on the interval $ (20,35) $ when $ t = 100.0 $, where $ u(t,x) $ is the numerical solution of $ (2) $