This paper deals with the amalgamated basic IS-LM business cycle model with Kaldor’s growth model to form an augmented model. Pertaining to substantial evidence, IS-LM model in paradigm with a specific economic extension (Kaldor-Kalecki Business cycle model in our case) provides an adept explanation of a developing but strong economy like that of our country. Occurring in the equation of capital accumulation, the two time delays are a result of the assumption in the investment function being both income and capital stock dependent in past period and maturity period. Investigating a model combined with capital accumulation is both interesting and important. From economist point of view, production without capital is impossible to even imagine. Moreover capital accumulation is impeccable to largescale production, specialisation and creation of employment opportunities. In our model ‘I’ the investment function, ‘S’ the savings function and ‘L’ the demand for money are depending linearly on their arguments. We adhere to a linear model, contrary to the popular belief of nonlinear models being the undisputed style for modern economics. The model is first shown to be mathematically and economically poised. The local stability of boundary and interior equilibrium points has been investigated. Three cases arise, pertaining to two time delays. System dynamics exhibits mutation under the influence of time delays and may clinch or discharge its local stability when subjected to the latter. Hopf bifurcation occurs when the delay parameter crosses a critical value. KeywordsBusiness cycle model, Time delay, Capital accumulation, IS-LM model, Hopf bifurcation.

中文翻译：

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具有两个时滞的增强型IS-LM线性商业周期模型中的Hopf分支

本文将合并的基本IS-LM商业周期模型与Kaldor的增长模型相结合，以形成增强模型。与大量证据有关，IS-LM模型具有特定的经济扩展范式（在我们的案例中为Kaldor-Kalecki商业周期模型）提供了对像我们国家这样的发展但强劲的经济的熟练解释。在资本积累方程中，这两个时间延迟是由于假设投资函数在过去的时期和到期期间都取决于收入和资本存量而产生的。研究与资本积累相结合的模型既有趣又重要。从经济学家的角度来看，没有资本的生产是无法想象的。而且，资本积累对于大规模生产是无可挑剔的，专业化和创造就业机会。在我们的模型“ I”中，投资函数，“ S”，储蓄函数和“ L”对货币的需求线性依赖于他们的论点。我们坚持使用线性模型，这与非线性模型是现代经济学无可争议的风格相反。该模型首先被证明具有数学和经济上的平衡性。已经研究了边界和内部平衡点的局部稳定性。出现了三种情况，涉及两个时间延迟。系统动力学在时延的影响下表现出突变，并且在受到后者的影响时可能会变形或释放其局部稳定性。当延迟参数超过临界值时，发生Hopf分叉。关键词：商业周期模型，时间延迟，资本积累，IS-LM模型，Hopf分叉。