On the chaotic nature of biological signals: linear and nonlinear data analysis of neuronal action potentials

Linear time invariant system analysis represents the educational core of the contemporary electrical engineer. While many of the analytical tools that are employed to perform linear analysis, i.e., mean, standard deviation, Fourier transforms, and the like, establish reliable and effective measures of prediction with regard to linear signals, biological signals such as those generated by the central nervous system, require additional considerations. Since the very nature of analysis is to make sense of what is and to apply it to what will be, the concept of predictability is of paramount concern. It has been established that various biological signals, including those used in neuronal communication, are in fact chaotic, making predictability a much more complex issue. A method of decomposing nonstationary and chaotic signals into stationary signals is proposed. By separating nonstationary signals into smaller time intervals, the segmented signal can be evaluated as a stationary signal. As a result, the stationary signal can be studied using linear and nonlinear analysis methodology, since observed chaotic parameters could otherwise be attributed to the nonstationarity. Using the neuronal signals from the pond snail Lynmaea stagnalis as a biological signal source, this research identifies and examines the relationships between linear and nonlinear systems.