Cyclicality and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global attractor and study limiting dynamics of the model. We estimate the Lyapunov exponents and get the exact formula for the Lyapunov dimension of the global attractor of this model analytically. With the help of delayed feedback control (DFC), the possibility of transition from irregular limiting dynamics to regular periodic dynamics is shown to solve the problem of reliable forecasting. At the same time, we demonstrate the complexity and ambiguity of applying numerical procedures to calculate the Lyapunov dimension along different trajectories of the global attractor, including unstable periodic orbits (UPOs).

经济固有的周期性和不稳定性可以表现为不规则的波动，包括​​混乱的波动，从长远来看，这大大降低了预测经济系统动态的准确性。我们专注于一种方法，与识别经济不规则波动的确定性内生机制相关。以一个中等规模的公司模型为例，我们展示了使用有效的分析和数值程序来计算其基于李雅普诺夫指数的不规则极限动力学的定量特征，例如维度和熵。我们使用一种分析方法来定位全局吸引子并研究模型的限制动力学。我们估计了李雅普诺夫指数，并通过分析得到了该模型全局吸引子的李雅普诺夫维数的精确公式。在延迟反馈控制（DFC）的帮助下，显示了从不规则限制动态过渡到规则周期动态的可能性，以解决可靠预测的问题。同时，我们展示了应用数值程序沿全球吸引子的不同轨迹（包括不稳定周期轨道 (UPO)）计算李雅普诺夫维度的复杂性和模糊性。