Stability and bifurcation analysis in a diffusive predator–prey model with delay and spatial average
Stability and bifurcation analysis in a diffusive predator–prey model with delay and spatial average
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DOI：
10.1002/mma.8853
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发表时间：
2022-11
影响因子：
2.9
通讯作者：
Yongli Song;Qingyan Shi
中科院分区：
文献类型：
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作者：
Yongli Song;Qingyan Shi
本文研究了在Neumann边界条件下空间平均和时滞对一类扩散捕食模型动力学的影响。与没有空间平均的模型相比，由于空间平均和时滞的共同作用，时滞诱导的Hopf分支在时滞的第一个临界值处是非齐次的，并出现时空模式.此外，我们发现，空间均匀和非均匀的周期图案可以切换不同的分歧参数值。此外，在齐次和非齐次Hopf分岔曲线的交点处出现了双Hopf分岔，在双Hopf分岔点附近的数值模拟中可以观察到空间非齐次的拟周期模式.对于一般的具有空间平均和时滞的反应扩散系统，给出了空间非齐次/齐次Hopf分支的规范形算法.
In this paper, we study the effect of spatial average and time delay on the dynamics of a diffusive predator–prey model under the Neumann boundary condition. Compared to the model without spatial average, the delay‐induced Hopf bifurcation at the first critical value of delay is nonhomogeneous due to the joint effects of spatial average and delay, and spatiotemporal patterns arise. Also, we show that the spatially homogeneous and nonhomogeneous periodic patterns may switch for different bifurcation parameter values. Moreover, a double Hopf bifurcation occurs at the intersection point of the homogeneous and nonhomogeneous Hopf bifurcation curves, and spatially nonhomogeneous quasi‐periodic patterns can be observed via numerical simulations near the double Hopf bifurcation point. The normal form algorithm for the spatially nonhomogeneous/homogeneous Hopf bifurcation is derived for a general reaction‐diffusion system with spatial average and delay.