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Lorenz Benzeri Doğrusal Olmayan Üç Boyutlu Yeni Bir Diferansiyel Denklem Sisteminin Kararlılık Analizi

Kaotik sistemler, başlangıç koşullarına duyarlı ve ölçülemeyecek karmaşıklıktaki dinamik sistemler olarak ifadeedilebilir. Başlangıç koşullarına olan duyarlılığının yanında kaotik sistemler, geniş bantlı ve periyodik olmayanbir özelliğe sahiptir. Bu özelliklerinden dolayı söz konusu bu sistemler, özellikle mühendislik alanlarında olmaküzere farklı bilim dallarında geniş uygulama alanına sahiptir. Bu makalede Lorenz benzeri doğrusal olmayan üçboyutlu yeni bir diferansiyel denklem sisteminin kararlılığı araştırılmıştır. Çalışmada öncelikle dikkate alınansistemin denge noktaları belirlenmiş ve kararlılık kriterleri Hurwitz koşulları kullanılarak incelenmiştir. Dahasonra, bu sistemin üstel kararlılığı için gerek ve yeter koşullar tartışılmıştır. Sonuç olarak, elde edilen sonuçlarilgili literatürde bulunan sonuçları içerir ve geliştirir.

Stability Analysis of a New Differential Equation System of Lorenz-like Nonlinear Three-Dimensional

Chaotic systems can be described as immeasurably complex dynamic systems which are sensitive to initial conditions. In addition to its sensitivity to initial conditions, chaotic systems have a broadband and non-periodicity. Because of these properties, these systems considered have a wide application area in different sciences, especially in engineering subjects. In this paper, the stability of a new differential equation system of Lorenz-like nonlinear three-dimensional, was investigated. In the study, firstly, the equilibrium points of the system which was taken into consideration were determined and the stability criteria were examined by using Hurwitz conditions. Then, the necessary and sufficient conditions for exponential stability of this system have been discussed. Consequently, the obtained results include and improve the results found in the related literature.

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