The interpretation of kernels―an overview

The kernel identification method is a powerful technique for mathematically representing the dynamic behavior of a nonlinear system. This technique has been applied to a number of physical and physiological systems. An important development which has enhanced the usefulness of the kernel method has been the interpretation of the internal structure of a system by examining the shapes of the higher-degree kernels. Examples of various nonlinear models with known structure are illustrated to show a repertoire of kernel shapes. Variations in parameters of these models result in well-defined changes in the shapes of the kernels. Also, examples are shown of kernels obtained from physiological systems to demonstrate how examination of kernel shapes can lead to accurate predictions of the dynamic behavior of the physiological system. Finally, limitations of the applicable range of the kernel identification method are discussed.