Complex biological oscillator

As an extension of the contribution of Dr. Stucki, I would like to bring attention to a rather complex biological oscillator. It deals with the case of invertebrate euryhaline species, clearly a case of integration of a biological system into its environment, that is, what the biologists call adaptation. 

All the complex behavior described so far in this Chapter arises from the diffusive coupling of the local dynamics which in the homogeneous case have simple fixed points as asymptotic states. If the local dynamics becomes more complex, the range of possible dynamic behavior in the presence of diffusion becomes practically unlimited. It is clear that coupling chaotic subsystems could produce an extremely rich dynamics. But even the case of periodic local dynamics does so. Diffusively coupled chemical or biological oscillators may become synchronized (Pikovsky et ah, 2003), or rather additional instabilities may arise from the spatial coupling. This may produce target waves, spiral patterns, front instabilities and several different types of spatiotemporal chaos or phase turbulence (Kuramoto, 1984). 

Some of the main examples of biological rhythms of nonelectrical nature are discussed below, among which are glycolytic oscillations (Section III), oscillations and waves of cytosolic Ca + (Section IV), cAMP oscillations that underlie pulsatile intercellular communication in Dictyostelium amoebae (Section V), circadian rhythms (Section VI), and the cell cycle clock (Section VII). Section VIII is devoted to some recently discovered cellular rhythms. The transition from simple periodic behavior to complex oscillations including bursting and chaos is briefly dealt with in Section IX. Concluding remarks are presented in Section X. 

Oscillating reactions, a common feature of biological systems, are best understood within the context of nonlinear chemical dynamics and chaos theory based models that are used to predict the overall behavior of complex systems. A chaotic system is unpredictable, but not random. A key feature is that such systems are so sensitive to their initial conditions that future behavior is inherently unpredictable beyond some relatively short period of time. Accordingly, one of the goals of scientists studying oscillating reactions is to determine mathematical patterns or repeatable features that establish relationships to observable phenomena related to the oscillating reaction. 

In the near future it can be expected that explanation of behavior of even complex chemical reactions will be attempted and types of oscillations will be more systematically classified. In this context, some of the previous work will probably be reevaluated. Since the role of chemical oscillations is clearly related to the biological systems via enzyme kinetics, chemical reaction studies will be centered no longer around the stationary states but the oscillatory solutions, both stable and unstable. 

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