For the current financial and economic systems characterized by unstable processes both in behavior and in structure. Causes of global financial instability rooted in imbalances and contradictions of international monetary and financial relations, which creates random perturbation of a different nature and give rise to unstable processes. Instability accompanied usually nonlinearities, which requires the development and application of innovative approaches to modeling processes analyzed. Thus, the urgency due to the need of improving conceptual approaches and modernization of methods of analysis and modeling processes postindustrial unstable financial and economic systems. The article aims to study the concept of modeling the nonlinear dynamics of economic and financial development and relevant economic and mathematical methods to ensure efficiency analysis of its behavior with regard to structural changes and external influences. In order to construct the concept of improved structure modeling method of nonlinear dynamics of financial and economic systems through the use of topology for structural construction investment by state space system in the area of greater dimension. The proposed method makes it possible to diagnose significant changes in the state that captures the transition from quantitative to qualitative changes. The set of values of corresponding small change dynamics falls into one equivalence class that is identified. This approach allows us to observe the structural changes with a change in behavior and detect structural imbalances. To diagnose the type of dynamics and assess the nature of behavioral change as components and the financial and economic systems generally allow fractal analysis. A method of diagnosing behavior improvement by integration of fractal analysis with Topological Spaces constructed on unit interval, to simulate the behavior of considering structural changes. 47 In order to take into account the influence of the environment on the dynamics of the financial and economic system, it is proposed to apply a method of leading indicators, which allows to improve the method of modeling and to specify the forecast twice, that is to determine the direction of dynamics and reduce the confidence interval twice. To solve the problems of the modern study of financial and economic dynamics based on advanced methods proposed design concept based on synergy topology, fractal geometry and leading indicators. This concept is based on the topological-fractal method simulation, which takes into account structural changes and leading indicators, taking into account external influences. The implementation of the concept makes it possible to increase the accuracy of diagnosis and prognosis of the dynamics of the financial and economic systems, which in turn are used in the construction of flexible management solutions that mitigate the crisis and effectively use favorable periods of financial and economic systems. It should be noted that the results have a theoretical value and practical significantce, since the combined deepen scientific justification and tools extend modeling of nonlinear dynamics of financial and economic systems and methods for analysis of structural changes and external influences. The methods are universal and suitable for use in the macro, meso and micro levels. Note that developed the concept design enables both qua