论文标题
空间平均水平对反应扩散系统的时空图案形成的影响
Effect of spatial average on the spatiotemporal pattern formation of reaction-diffusion systems
论文作者
论文摘要
来自细胞生物学或生态学的反应扩散模型中的某些量取决于密度函数的空间平均值，而不是局部密度函数。我们表明，这种非局部空间平均值可以诱导恒定稳态的不稳定性，这与经典的图灵不稳定性不同。对于具有空间平均值的一般标量方程，严格证明了稳态分叉的发生，并给出了确定分叉方向和分叉稳态稳定性的公式。对于两个物种模型，由于恒定平衡的空间非均匀的HOPF分叉，可能会出现空间非均匀的时间周期轨道。使用非局部合作的Lotka-Volterra模型和非局部Rosenzweig-Macarthur Predator-Prey模型的示例用于证明空间非均匀模式的分叉。
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of constant steady state, which is different from classical Turing instability. For a general scalar equation with spatial average, the occurrence of the steady state bifurcation is rigorously proved, and the formula to determine the bifurcation direction and the stability of the bifurcating steady state is given. For the two-species model, spatially non-homogeneous time-periodic orbits could arise due to spatially non-homogeneous Hopf bifurcation from the constant equilibrium. Examples from a nonlocal cooperative Lotka-Volterra model and a nonlocal Rosenzweig-MacArthur predator-prey model are used to demonstrate the bifurcation of spatially non-homogeneous patterns.
