Synchronization Phenomena and Circuit Experiment of Star-Coupled van der Pol Oscillators with Additional Oscillators
Minh Hai TRAN Yoko UWATE Yoshifumi NISHIO
Tokushima University
1 Introduction
In our previous study, we investigated synchroniza- tion phenomena observed by adding different frequency van der Pol oscillators coupled with star combination.
By computer simulations, we confirmed some of oscil- lators in the system were synchronized at anti-phase.
In this study, we carry out circuit experiments with 4 van der Pol oscillators system. In addition, we exam- ine in detail 4 van der Pol oscillators and 5 van der Pol oscillators.
2 Circuit Model
The circuit model used in the first pattern is shown in Fig. 1. Three van der Pol oscillators are connected as the star combination. In addition, we add a differ- ent frequency oscillator to the star-coupled van der Pol oscillators. We change the frequency of the 4th oscil- lator and investigate the influence of the 4th oscillator to the overall star circuit.
i R1 C v 1
v 2
v 3
v v 4
i R3 i R4
i R2
v R 1 R
2L
2L 2L
2L 2L 2L 2L 2L
(4) (2)
(1) (3)
I 4A I 4B I 3B
I 2A
I 1A
I 2B
C C
0
I 3A
C n: number of oscillator. (n: 1-4)
Fig. 1 Circuit model.
Three van der Pol oscillators are connected as the star combination. In addition, we add a different fre- quency oscillator to the star-coupled van der Pol oscil- lators. We change the frequency of the 4th oscillator and investigate the influence of the 4th oscillator to the overall star circuit.
3 Simulation Result
The amplitudes of the oscillator are shown in the Figs. 2. In Fig. 2, when the ω increase from 1 to 1.2, the amplitudes of the 3rd and the 4th oscillator become gradually smaller. Next, when the ω is increased to 1.4, the amplitudes of the 3rd and the 4th oscillator are perfect stop. When ω above 1.4, the amplitudes of the 4th oscillator go on increasing. However, the
amplitudes of the 3rd oscillator are almost unchanged.
Fig. 2 Amplitude of oscillator 3 and oscillator 4.
We build a real circuit as Fig. 4 to confirm the results above. The frequency ω is changed by altering the tunnel diode of the fourth oscillator. Figure 4 shows one of my obtained circuit experimental results.
x 1
x
2
x 3
x 4
Fig. 3 Simulation result.
Fig. 4 Circuit experimental result.
In Fig. 4, circuit experimental result also fit theoret- ical analysis results with computer calculations. The 3th oscillators stop.
4 Conclusion
We have investigated synchronization phenomena and oscillation of five oscillators with different frequen- cies. By carrying out computer simulations and circuit experiments, we have confirmed that oscillation of the 3th oscillators are death by increasing ω.
平成
