# Investigation the Critical Levels in Development of the Complex Systems with Shifted Arguments for their Optimal Control

## TL;DR

This paper explores the critical levels and potential catastrophes in complex systems across various fields, using mathematical models to identify and control these phenomena for stable development.

## Contribution

It introduces new mathematical modeling techniques for analyzing critical levels in complex systems with shifted arguments, aiding in their optimal control.

## Key findings

- Identification of critical levels in diverse complex systems.
- Development of models for predicting system catastrophes.
- Strategies for controlling complex systems to prevent instability.

## Abstract

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels in a development of complex systems for various natures associated with diverse complicated factors, in particular with shifted arguments of the system. Intensive research in this direction and developed techniques may optimize management of the complex systems in financial-economic, natural and other fields. Construction of adequate mathematical models for development of complex systems, critical modes and their effective control are important tasks for a wide range of contemporary issues as shown in paper on examples. Critical levels in development of economic, banking, technical, political and other systems are necessary to determine and anticipate, to manage their system requirements and provide stable development, without being hit in a critical situations, leading to growing oscillations of the system settings.

---
Source: https://tomesphere.com/paper/1704.01424