In nature, we can observe various nonlinear phenomena such as chaos and reaction diffusion systems. These phenomena can be partly modeled. For example, the Lorentz system can be modeled in terms of a nonlinear oscillator. Moreover, a spatiotemporal system can also be modeled in terms of a coupled oscillator system. In this system, the oscillators connect each other.
Technological applications using a nonlinear oscillator system such as chaotic communication and data encryption has been studied. So that apply the nonlinear oscillator system for such applications, a nonlinear oscillator model must be fabricated on integrated circuit. Therefore, a 2-prey 1-predator Lotka-Volterra system that has a simple expression is fabricated, and this system represents various nonlinear oscillations.
In this thesis, I fabricated an analog integrated circuit that implements a 2-prey 1-predator Lotka-Volterra oscillator. Since the integrated circuit has a compact structure, many circuits can be arranged on a silicon chip. Thus, a two-dimensional structure, that is a diffusive Lotka-Volterra system, can be constructed. In this system, I estimated spatial instability conditions that the system represents a spatial behavior such as spatial localized patterns by theoretical analysis. Moreover, I conducted numerical simulations under the spatial instability conditions, and spatial localized patterns were obtained in the diffusive Lotka-Volterra system.