• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.1
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• pp.87-92
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• 2016

Van der Pol's oscillators is non-conservative oscillator that having nonlinear damping phenomena. The energy of its system is dissipative at a high amplitude whereas its system creates the energy at low amplitude. In order to identify another behaviors in the Van der Pol oscillator, the periodic external force applied in the Van der Pol oscillator. This paper confirms the pattern of variation for the limit cycle according to parameter variation in order to identify another behaviors in the Van der Pol oscillator.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.2
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• pp.191-196
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• 2016

Van der Pol's oscillators is non-conservative oscillator that having nonlinear damping phenomena. The energy of its system is dissipative at a high amplitude whereas its system creates the energy at low amplitude. This paper deals with the Van der Pol oscillator model with a fractional order when the external force apply into Van der Pol oscillator. This paper confirms the status of variation for the limit cycle according to the parameter variation of fractional order in the Van der Pol oscillator that can be represented by fractional differential equation.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.1
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• pp.81-86
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• 2016

Three hundred years ago, the fractional differential equation that is one of concept of fractional calculus released. Now, many researchers continue to try best effort applying into the control engineering, mathematics and physics. In this paper, the dynamics equation which is represented by Van der Pol, represent integer order and fractional order that having real order. Then this paper performs the comparisons between integer and real order as time series and phase portrait according to variation of parameter value for real order.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.706-709
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• 2005

We study the adaptive stabilization of the Van der Pol equation. A parameter update law is designed by the immersion and invariance method, and is used in conjunction with both the feedback linearization and backstepping control laws. Simulation results show that the responses obtained in the adaptive case are very similar to the known parameter case, and the parameter estimator converges to the true value.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.8
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• pp.1692-1699
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• 2004

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. We also show computer simulation results of Arnold equation, Chua's equation, Hyper-chaos equation, Hamilton equation and Lorenz chaos trajectories with one or more Van der Pol obstacles.

• The Transactions of the Korea Information Processing Society
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• v.3 no.4
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• pp.877-882
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• 1996

The effects of periodic and chaotic behaviour in the Bonhoeffer-Van der Pol (BVP) oscillation of the nerve membrane driven by a periodic stimulating current A1 coswtare investigated through hardware implementation.For hardware implementation of the BVP model. real element values were escaled with computer simulation results to determine the parameter real value.As the parameter A1 varied in the range 0 to 1.3, the BVP model showed an ordinary and reversed period-doubling cascade and a chaotic state. At the low driving amplitude ofa1 the period-doubling showed and at the high driving amplitude of A1 the chaotic state occured. To analyse the BVP model for chaotic behaviour Phase Plane, Time series are used to verify that properties.

• The Journal of the Korea institute of electronic communication sciences
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• v.1 no.1
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• pp.49-55
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• 2006

Applied by periodic Stimulating Currents in Bonhoeffer -Van der Pol(BVP) model, chaotic and periodic phenomena occured at specific conditions. The conditions of the chaotic motion in BVP comprised 0.7182< $A_1$ <0.792 and 1.09< $A_1$ <1.302 proved by the analysis of phase plane, bifurcation diagram, and lyapunov exponent. To control the chaotic motion, two methods were suggested by the first used the amplitude parameter A1, $A1={\varepsilon}((x-x_s)-(y-y_s))$ and the second used the temperature parameterc, $c=c(1+{\eta}cos{\Omega}t)$ which the values of ${\eta},{\Omega}$ varied respectlvly, and $x_s$, $y_s$ are the periodic signal. As a result of simulating these methods, the chaotic phenomena was controlled with the periodic motion of periodisity. The feasibilities of the chaotic and the periodic phenomena were analysed by phase plane Poincare map and lyapunov exponent.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.511-523
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• 2007

We consider a two parametric family of the planar systems with the form $\dot{x}=P(x,\;y)+{\in}_1p_1(x,\;y)+{\in}_2p_2(x,\;y)$, $\dot{y}=Q(x,\;y)+{\in}_1p_1(x,\;y)+{\in}_2p_2(x,\;y)$, where the unperturbed equation(${\in}_1={\in}_2=0$) is assumed to have at least one periodic solution or limit cycle. Our aim here is to study the behavior of the system under two parametric perturbations; in fact, using the Poincare-Andronov technique, we impose conditions on the system which guarantee persistence of the periodic trajectories. At the end, we apply the result on the Van der Pol equation ; where, we consider the effect of nonlinear damping on the equation. Also the Hopf bifurcation for the Van der Pol equation will be investigated.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.937-941
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• 2005

In this paper, we propose a chaotic underwater robots that have unstable limit cycles in a chaos trajectory surface with Arnold equation, Chua's equation. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. We also show computer simulation results of Arnold equation and Chua's equation chaos trajectories with one or more Van der Pol obstacles

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.817-819
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• 1995

Applied by periodic Stimulating Currents in Bonhoeffer-Van der Pol(BVP) model, chaotic and periodic phenomena occured at specific conditions. The conditions of the chaotic motion in BVP comprised 0.7182< $A_{1}$ <0.792 and 1.09< $A_{1}$ <1.302 proved by the analysis of phase plane, bifurcation diagram, and lyapunov exponent. To control the chaotic motion, two methods were suggested by the first used the amplitude parameter $A_{1}$,$A_{1}={\varepsilon}((x-x_{s})-(y-y_{s}))$ and the second used the temperature parameter c, c=c$(1+ {\eta}cos{\Omega}t)$ which the values of $\eta$, ${\Omega}$ varied respectlvly, and $x_{s}$, $y_{s}$ are the periodic signal. As a result of simulating these methods, the chaotic phenomena was controlled with the periodic motion of periodisity. The feasibilities of the chaotic and the periodic phenomena were analysed by phase plane and lyapunov exponent.