Research on linear and nonlinear IS-LM models has been resonating under synonymous perspectives, confined to bifurcations and intangible relations to economic work systems. Trifle discussion exists on how choice of linear/nonlinear models affects policy making and almost no elaboration on framing an economic system within a linear and nonlinear structure to analyze their effect separately. Parameters surrounding IS-LM model like adjustment coefficients, depreciation of capital stock etc. have not been given due spotlight, given the audacity they possess to modulate system dynamics. In counteraction, we have investigated an augmented IS-LM model with two-time delays in capital accumulation equation. This model is subjected to linear and nonlinear arguments of investment, savings and liquidity function giving rise to M1(linear) and M2(nonlinear) models. They undergo hopf bifurcation for different values of delay parameters τ1 and τ2. Our study accentuates the following aspects(1) In a neophyte attempt, comparing the dynamics of a linear and nonlinear business cycle model in an environment as similar as possible, when τ1 and τ2 are the bifurcating parameters. (2) Parameter sensitivity analysis for both models. (3) Non linearity in savings function, which is a sparse event so far. Our findings reveal that (1) Non-linearity elevates system sensitivity and M2 model attains stability easily in the long run for dual delays, while for single delay M1 model has this feat. (2) M2 model encapsulates recurring cyclic behavior while M1 model is not capable of generating the same and demonstrates motifs of either stability or instability. (3) Parameter sensitivity analysis reveals that both the models are most vulnerable when (3a)Value of depreciation of capital stock is decreased. (3b) Money supply and propensities to investment are increased. (4) how aforementioned information can be utilized for crafting economic policies for linear/nonlinear economies, especially curated for their modus operandi. Numerical simulations follow.

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线性和非线性商业周期模型的比较分析：对系统动力学，经济和政策制定的总体影响

线性和非线性IS-LM模型的研究在同义的观点下引起了共鸣，仅限于分叉和与经济工作系统的无形关系。存在关于线性/非线性模型的选择如何影响政策制定的琐碎讨论，几乎没有阐述将线性或非线性结构内的经济系统框架化以分别分析其影响的细节。围绕IS-LM模型的参数（例如调整系数，资本存量折旧等）并未得到应有的关注，因为它们具有调节系统动力学的勇气。作为对策，我们研究了资本积累方程中具有两次延迟的增强型IS-LM模型。该模型受线性和非线性投资论证的影响，储蓄和流动性函数产生了M1（线性）和M2（非线性）模型。对于延迟参数τ1和τ2的不同值，它们会进行Hopf分叉。我们的研究着重于以下几个方面：（1）在新手尝试中，当τ1和τ2是分叉参数时，在尽可能相似的环境中比较线性和非线性商业周期模型的动力学。（2）两种模型的参数敏感性分析。（3）储蓄函数中的非线性，到目前为止是稀疏事件。我们的发现表明：（1）非线性提高了系统灵敏度，M2模型从长远来看很容易获得稳定性，对于双重延迟，而对于单一延迟，M1模型具有这一壮举。（2）M2模型封装了周期性的循环行为，而M1模型则无法产生周期性的行为，并表现出稳定性或不稳定性的图案。（3）参数敏感性分析表明，当（3a）资本存量的折旧价值降低时，两个模型都最容易受到影响。（3b）货币供应量和投资倾向增加。（4）如何将上述信息用于制定线性/非线性经济体的经济政策，尤其是针对其惯性方式进行策划。数值模拟如下。（4）如何将上述信息用于制定线性/非线性经济体的经济政策，尤其是针对其惯常操作方式进行策划。数值模拟如下。（4）如何将上述信息用于制定线性/非线性经济体的经济政策，尤其是针对其惯性方式进行策划。数值模拟如下。