Title :
Resonant phenomena in coupled oscillators arising in the interaction and production of two enzymes
Author_Institution :
Dept. of Math., Southern Illinois Univ., Carbondale, IL, USA
Abstract :
A class of diffusively coupled oscillators is discussed. The model is governed by reaction-diffusion equations with nonlinear boundary conditions. The two linear uncoupled equations describe the diffusion process, while the nonlinear boundary conditions describe all reaction and interaction. By using the boundary conditions, the system can be translated into two uncoupled oscillators of two dimensions. It is found that the Hopf bifurcations are always degenerate due to the internal resonance of the system
Keywords :
bifurcation; biotechnology; nonlinear control systems; oscillators; process control; proteins; resonance; boundary conditions; coupled oscillators; degenerate Hopf bifurcations; diffusion process; diffusively coupled oscillators; enzyme interaction; enzyme production; internal resonance; linear uncoupled equations; nonlinear boundary conditions; reaction-diffusion equations; resonant phenomena; uncoupled oscillators; Bifurcation; Biochemistry; Biomembranes; Boundary conditions; Couplings; Ear; Mathematics; Nonlinear equations; Oscillators; Production;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.914094
