Abstract
This paper studies the stability of complex-valued nonlinear differential system. The stability criteria of complex-valued nonlinear autonomous system are established. For the general complex-valued nonlinear non-autonomous system, the comparison principle in the context of complex fields is given. Those derived stability criteria not only provide a new method to analyze complex-valued differential system, but also greatly reduce the complexity of analysis and computation.
Highlights
This paper studies the stability of complex-valued nonlinear differential system
The stability of differential system has been studied by many researchers, for example, [1,2,3,4,5,6] and references therein
The common setting adopted in aforementioned works is always in real number fields; namely, the objects of study are real-valued differential systems
Summary
The stability of differential system has been studied by many researchers, for example, [1,2,3,4,5,6] and references therein. The usual method analyzing complex-valued system is to separate it into real part and imaginary part and recast it into an equivalent real-valued system (see [14, 15] and references therein). The comparison principle of complex-valued nonautonomous differential system is given Those derived stability criteria generalize some known results in literature and greatly reduce the complexity of analysis and computation. The stability conditions of a class of complexvalued nonlinear systems are presented.
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