Chaos, antimonotonicity and coexisting attractors in Van der Pol oscillator based electronic circuit

Sarkar, Saumendra Sankar De; Sharma, Ajay K.; Chakraborty, Saumen

doi:10.1007/s10470-021-01934-8

Cited by 8 publications

(3 citation statements)

References 50 publications

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“…Bifurcation analysis for systems exhibiting chaos or hyperchaos is useful to get illuminated on the various qualitative properties like oscillations, quasi-periodicity, chaoticity, and hyperchaoticity when the parameters take various values in specified intervals [24][25][26]. Our research study also shows that the new hyperchaotic system exhibits multistability, which is a special property of coexistence of attractors for a selected set of values for the parameters but differing sets of values for the initial data of the trajectories [27,28].…”

Section: Introductionmentioning

confidence: 93%

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

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With the swift advancement of chaos theory, the modeling, chaotic oscillations, and engineering applications of chaotic and hyperchaotic systems are important topics in research. In this research paper, we elucidate our findings of a new four-dimensional two-scroll hyperchaotic system having only two quadratic nonlinearities and carry out a detailed bifurcation study of the proposed dynamical model. Also, an electronic circuit has been constructed for the new system using MultiSim (Version 14). The implementation of the new 4-D hyperchaotic system in a field-programmable gate array (FPGA) is performed herein by applying two numerical methods, viz. Forward Euler Method and Trapezoidal Method. The experimental results show a good match with the simulated hyperchaotic attractors. We also provide details of the hardware resources used for an FPGA Basys 3 Xilinx Artix-7 XC7A35T-ICPG236C.

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Section: Introductionmentioning

confidence: 93%

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

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“…16 is the inverse function of Eq. (21)(22)(23). Obviously, the solution of the special periodic motion x(τ ) = Am(τ + ψ, b) is a periodic function except that for b = 1 2 , where ψ is the amplitude which is decided by initial condition.…”

Section: Solution Of the Special Periodic Orbitmentioning

confidence: 99%

“…Also, Van der Pol Oscillator [17] is a classical oscillator with nonlinear damping, which exhibits a limit circle [18]. Even some recent studies concentrate on dynamics of Van der Pol oscillator, such as its complex bifurcation and hysteresis [19], multistability and symmetry breaking coupled to a Duffing oscillator [20], antimonotonicity and coexisting attractors under the inclusion of an active RC section [21] and so on. As a classical model of cylindrical system, mathematical pendulum also has attracted much attention for a long time.…”

Section: Introductionmentioning

confidence: 99%

The complicated dynamical behaviours of a geometrical oscillator with a mass parameter

Huang

Cao

2023

Preprint

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In this paper, we consider a special kind of geometrical nonlinear oscillator with a mass parameter admitting two different dynamical states leading to a double-valued potential energy. A cylindrical manifold is introduced to formulate the equation of motion to describe the distinguished dynamical behaviours. With the help of Hamiltonian, the complex bifurcations are demonstrated with the varying of parameters including periodic solutions, the steady states and the blowing up phenomenon near θ = ± π/2 to infinity. A toroidal manifold is introduced to map the infinities into (0, ±2, 0) on the torus exhibiting saddle-node-like behaviour, where the uniqueness of solution is failed, for which a special ‘collision’ parameter is introduced to define the possible motion leaving from the infinities. A numerical method which is proposed to get solution near the infinity where Runge-Kutta method fails, is employed to get the bifurcation diagrams using Poincaré sections for the perturbed system to exhibit the complex dynamics including the co-existence of periodic solutions, the chaos from the coexisted periodic doubling and also the instant chaos from the coexisted periodic solutions. The results demonstrated herein this paper provide a brand new insight into the understanding of enriched nonlinear dynamics and an essential explanation about ‘collision’ of mechanical system with both the geometrical and mass parameters.

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Rich Dynamical Behavior in a Simple Chaotic Oscillator Based on Sallen Key High-Pass Filter

Chakraborty

Sarkar²

2023

Circuits Syst Signal Process

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Chaos, antimonotonicity and coexisting attractors in Van der Pol oscillator based electronic circuit

Cited by 8 publications

References 50 publications

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

The complicated dynamical behaviours of a geometrical oscillator with a mass parameter

Rich Dynamical Behavior in a Simple Chaotic Oscillator Based on Sallen Key High-Pass Filter

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