Computer and Hardware Modeling of Periodically Forced -Van der Pol Oscillator Computer and Hardware Modeling of Periodically Forced -Van der Pol Oscillator

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Yoshizawa, An active pulse transmission line simulating nerve axons. Acoustics Woafo, Melnikov chaos in a periodically driven Raylegy-Duffing oscillator.

Like many areas of engineering, power electronics is mainly motivated by practical applications, and it often turns out that a particular circuit topology or system implementation has found widespread applications long before it is thoroughly analyzed and most of its subtleties are uncovered [ 3031 ].

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On the Van Der Pol Oscillator: an Overview

Nature Woafo, Dynamics and synchronization of coupled self-susteained electromechanical devices. The -Van der Pol oscillator is a very significant classical model circuit that has been studied and even modified in some studies as reported by King et al.

Stewart, Nonlinear Dynamics and Chaos. A -Van der Pol oscillator or extended Van der Pol oscillator is the nonlinear oscillator with fifth-order nonlinear term.

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Physica A A 36 We also generate phase portraits for the triple-well and double-well attractors of the system. Cai, Path integration of the Duffing-Rayleigh oscillator subject isostasia yahoo dating harmonic and stochastic excitations.

This paper presents the chaotic dynamics of -Van der Pol oscillator via electronic design, simulation, and hardware implementation.

Khodabakhsh, A homotopy analysis method for limit cycle of the van der Pol oscillator with delayed amplitude limiting. Therefore, the -circuits which have rich dynamics and may have important applications in secure communications, random number generations, cryptography, and so forth have been practically implemented.

Among the 2-dimensional periodically forced oscillators, the most extensively studied examples are the Van der Pol oscillators [ 78 ], Duffing oscillators [ 9 ], and Rayleigh oscillators [ 10 ]. Its numerical simulation has been studied extensively by Siewe Siewe et al.

On the Van Der Pol Oscillator: an Overview

Nesterov, Self-sustained oscillations of Rayleigh and van der Pol oscillators with moderately large feedback factors. In the past three decades, implementation of chaotic systems in power electronics has gone through intense development in many aspects of technology [ 27 — 29 ], including power devices, control methods, circuit design, computer-aided analysis, passive components, and packaging techniques.

Broadband synchronization, Physica D Yang, Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator. Turukina, Coupled van der Pol-Duffing oscillators: Physica D Narm, A new state observer for two coupled van der Pol oscillators, Int.

Lai, Analytical approximate periodic solutions for two-degree-of-freedom coupled van der Pol-Duffing oscillators by extended homotopy analysis method. Christopher, Limit cycles in highly non-linear differential equations.

Lienard, Etude des oscillations entrenues. The aim of this paper is to design, simulate, and implement periodically forced -Van der Pol oscillator by transforming the state equations into electronic circuit via analog components modeling. The results obtained are found to be in good agreement with numerical simulation results.

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Lauterborn, Period doubling cascade and devil staircases of the driven van der Pol oscillator. Brief description of the conditions for stability of fixed points for unperturbed system is discussed in the next section. Fang, Stochastic bifurcation in Duffing-Van der Pol oscillators.

Roman, Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol-Duffing oscillators. Theory Application 48 Automation and Systems 9 Guo, Investigation of chaotic motion in histeric non-linear suspension system with multi-frequency excitations.

The rest of the paper is organized as follows: Fitzhugh, Impulses and physiological states in theoretical models of nerve membranes.

Kom, Analog circuit implementation and synchronization of a system consisting of a van der Pol oscillator linearly coupled to a Duffing oscillator. Deghghan, Numerical solution of the controlled Rayleigh nonlinear oscillator by the direct spectral method.

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Many works on self-excited, parametrically excited, and externally excited oscillators are also investigated in the literature. Cveticanin, On the truly nonlinear oscillator with positive and negative damping.

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Nonlinear Dynamics 70 Introduction In recent years the study of chaotic phenomena in self-excited oscillators with parametric and external-excitation has attracted much attention [ 1 — 6 ]. The condition for stability of the fixed points is also computed and the method of multiple time scale is used to investigate the dynamical behaviour of the system.

Nesterov, Self-sustained oscillations of a highly non-linear system.

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Finally, Section 5 concludes the paper. Thus, the system can therefore be expressed as a set of first-order differential equations of the form which corresponds to an integrable Hamiltonian system with the potential function in 2 and whose associated Hamiltonian function is From 3 and 4we can compute for the fixed points and analyze their stabilities after some algebraic manipulations using the following conditions.

Analysis of the Unperturbed System The general form of second-order differential equation of Van der Pol systems is given as where is the damping parameter and and are amplitude and angular frequency, respectively, and its potential can be expressed in Taylor series as where, and are constant parameters.