A New Paradigm on the Qualitative Behavior of Chua’s Circuit

Year 2022, Volume: 12 Issue: 2, 177 - 182, 24.12.2022

Muzaffer Ateş Muhammet Ateş

Abstract

Today, the qualitative behavior of dynamical systems is a very important subject of control theory. Based on this, we consider the stability and instability properties of the equilibrium points of Chua’s circuit under suitable conditions by the Lyapunov direct method. This method gives us qualitative information directly without solving the given systems. From this circuit, we construct suitable energy or candidate Lyapunov function and then apply the method as a tool to investigate the global asymptotic stability and instability of the system. We also determine under which conditions the system behaves as a chaotic system or a memristor. In this study, we realized that an unforced dissipative dynamical system with bounded initial states has zero solution or motion at infinity. Some simulation results and examples are given to verify the obtained theoretical predictions

Keywords

Chua’s circuit, Lyapunov stability, Nonlinear RLC circuit, Memristor,

Chua Devresinin Kalitatif Davranışı Üzerine Yeni Bir Paradigma

Abstract

Günümüzde dinamik sistemlerin niteliksel davranışı, kontrol teorisinin çok önemli bir konusudur. Buna dayanarak, Lyapunov direkt yöntemi ile Chua devresinin (üçüncü derece sistem) kararlılık ve kararsızlık özelliklerini uygun koşullar altında ele alıyoruz. Bu yöntem, verilen sistemleri çözmeden bize doğrudan niteliksel bilgi verir. Bu devreden uygun bir enerji (Lyapunov) fonksiyonu oluşturuyoruz ve daha sonra sistemin global asimptotik kararlılığını ve kararsızlığını araştırmak için bir araç olarak yöntemi uyguluyoruz. Ayrıca sistemin hangi koşullar altında bir memristor gibi davrandığını da belirleriz. Bu çalışmada, zorlamasız enerji tüketen dinamik bir sistemin (sınırlı başlangıç durumları) sonsuzda sıfır çözüme (hareket) sahip olduğunu fark ettik. Elde edilen teorik tahminleri doğrulamak için bazı simülasyon sonuçları ve örnekler verilmiştir.

Keywords

Chua devresi, Lyapunov kararlılığı, Memristor, Doğrusal olmayan RLC devresi, Chua’s circuit, Lyapunov stability, Nonlinear RLC circuit

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