The aim of the present paper, how the people behave towards the offer of two products in two different patches. In this work, an innovation diffusion model with six-compartments for two different patches is proposed. There is a delay in the adoption of product-1 in patch-2 and delay of adoption of product-2 in patch-1. The entire population in both the patches is classified into three different groups (i) non-adopter (ii) adopter of product-1 (iii) adopter of product-2. Dynamical behavior of the proposed system is studied, and Basic influence numbers (BINs) of the model are calculated. Stability analysis is executed for all the possible equilibrium points with and without delays. Hopf bifurcation analysis is too carried out taking the delay of adoption to adopt the product-1 in patch-2, and product-2 in patch-1 are bifurcation parameter and obtained the threshold values. Moreover, sensitivity analysis is carried out for the system parameter used in the interior equilibrium. Finally, exhaustive numerical simulations have been carried out by utilizing MATLAB, to supports analytical results.

中文翻译：

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具有两个不同补丁中两个竞争产品的相互作用和采用延迟的创新扩散模型

本文的目的是，人们如何对待两种不同补丁的两种产品。在这项工作中，提出了针对两个不同补丁的六格创新扩散模型。补丁2中采用product-1的延迟和补丁1中采用product-2的延迟。两个补丁中的整个种群分为三个不同的组（i）非采用者（ii）产品1的采用者（iii）产品2的采用者。研究了所提出系统的动力学行为，并计算了模型的基本影响数（BINs）。对所有可能的平衡点（有或没有延迟）执行稳定性分析。对于补丁2中采用产品1的情况，也进行了Hopf分叉分析，考虑了采用的延迟。补丁1中的乘积2和乘积2是分叉参数，并获得了阈值。此外，对内部平衡中使用的系统参数进行灵敏度分析。最后，利用MATLAB进行了详尽的数值模拟，以支持分析结果。