Coupling

virtual-virtual coupling

Based on the experimental result, we select the dual-feedback oscillator to finish the modulating and coupling process. First, we will finish the virtual-virtual coupling. So different initial values of parameters are set to the simulation to form two e-oscillators which are of the same properties.

Then how could they adjust to each other and be strongly coupled or synchronized? We think about the dynamic equilibrium of wolf and rabbit. If the number of wolves increases rapidly, lots of rabbits would be eaten and the number would reduce. Faced with the decrease of prey, the quantity of wolves would also cut down. On the contrary, rabbits would multiply with fewer natural predators. Cycling like these, wolf and rabbit would finally reach the dynamic balance.

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According to the above mechanism, we make the two e-oscillators pass the parameters and affect each other. In terms of the transfer function, with the enhancement of the light intensity, the expression of lacI will reduce, which is proportional to the other e-oscillator’s light intensity. It means that the illumination intensity of e-oscillator 2 will decrease and the corresponding lacI will increase. Then lacI will also be inversely linked to the e-oscillator 1. With the circulation and regulation, the two e-oscillator will be coupled or synchronized gradually.

To achieve the process of coupling or synchronization, we write programs in MATLAB and get the simulation result shown in Figure 3.

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Figure 3. Simulation result of virtual-virtual coupling.