Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications
Othman Abdullah Almatroud, Али А. Шукур, Viet–Thanh Pham, Giuseppe Grassi
Abstract
We explore an oscillator with nonlinear functions and equilibrium lines that displays chaos. The equilibrium stability and complexity of the oscillator have been analysed and investigated. The presence of multiple equilibrium lines sets it apart from previously reported oscillators. The synchronization of the oscillator is considered as an application for secure communications. An observer is designed by considering a transmitted signal as a state, in other words, by injecting a linear function satisfying Lipschitz’s condition to the proposed oscillator. Moreover, the adaptive control of the new oscillator is obtained.
Topics & Concepts
Synchronization (alternating current)Control theory (sociology)Nonlinear systemLipschitz continuityObserver (physics)Line (geometry)Delay line oscillatorStability (learning theory)Function (biology)MathematicsTopology (electrical circuits)Computer scienceMathematical analysisPhysicsTelecommunicationsLocal oscillatorControl (management)Quantum mechanicsCombinatoricsEvolutionary biologyRadio frequencyBiologyMachine learningGeometryArtificial intelligenceNonlinear Dynamics and Pattern FormationChaos control and synchronizationstochastic dynamics and bifurcation