Abstract
This chapter discusses stability technique and thought provocative dynamical systems. Since 1940, there is a continuous growth in stability conditions of linear differential systems. The chapter presents a very simple stability conditions that includes the earlier stability conditions for linear systems. In addition, it is also applicable for special type of nonlinear systems that are mathematical models of thought provocative phenomena, such as chemical systems, compartmental systems, eco-systems, economic systems, social systems, etc. The presented stability conditions illustrate several intrinsic problems that are of practical interest, for example, complexity vs. stability, measurability of complexity, sensitivity of stability, etc. It bridges the gap between the two mathematical stability conditions and the gap between the mathematical conditions and certain real life problems.
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