Search results for "Chua circuit"

showing 3 items of 3 documents

Hidden and self-excited attractors in radiophysical and biophysical models

2017

One of the central tasks of investigation of dynamical systems is the problem of analysis of the steady (limiting) behavior of the system after the completion of transient processes, i.e., the problem of localization and analysis of attractors (bounded sets of states of the system to which the system tends after transient processes from close initial states). Transition of the system with initial conditions from the vicinity of stationary state to an attractor corresponds to the case of a self-excited attractor. However, there exist attractors of another type: hidden attractors are attractors with the basin of attraction which does not have intersection with a small neighborhoods of any equ…

Chua circuitskaaosteoriapancreatic beta-cellvirtapiiritattraktoritradiophysical generatoroskillaattoritbiofysiikkaNonlinear Sciences::Chaotic Dynamicshidden attractorsbifurkaatiosäteilyfysiikkamultistabilityself-excited attractorskatastrofiteoriamatemaattiset mallitdifferentiaaliyhtälöt
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Scenario of the Birth of Hidden Attractors in the Chua Circuit

2017

Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.

Mathematics::Dynamical Systemsclassification of attractors as being hidden or self-excitedChaoticFOS: Physical sciences01 natural sciences010305 fluids & plasmassymbols.namesake0103 physical sciencesAttractorStatistical physicsHidden Chua attractor010301 acousticsEngineering (miscellaneous)Nonlinear Sciences::Pattern Formation and SolitonsBifurcationMathematicsEquilibrium pointHopf bifurcationta213Applied Mathematicsta111pitchfork bifurcationChua circuitNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsPitchfork bifurcationclassificationbifurcation theoryModeling and Simulationsubcritical Hopf bifurcationsymbolsChaotic Dynamics (nlin.CD)Merge (version control)International Journal of Bifurcation and Chaos
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Hidden attractors in Chua circuit: mathematical theory meets physical experiments

2022

AbstractAfter the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaotic attractors of the considered dynamical models are rather artificial, computer-induced objects, i.e., they are generated not due to the physical nature of the process, but only by errors arising from the application of approximate numerical methods and finite-precision computations. Further justification for the possibility of a real exi…

kaaosteoriaApplied MathematicsMechanical Engineeringelektroniset piiritAerospace EngineeringattraktoritOcean EngineeringChua circuitfysikaaliset ilmiöthidden attractorsradiophysical experimentControl and Systems Engineeringmatemaattiset mallitdynaamiset systeemitElectrical and Electronic EngineeringbifurcationsNonlinear Dynamics
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