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Author(s): Grossberg, S. |
Year: 1977
Citation: Journal of Mathematical Analysis and Applications, 58, 152-173.
Abstract: This paper continues the discussion of singular perturbation solutions of nerve impulse equations begun in [1]. Phase specie analysis is used to study a general model of a biological process (e.g., nerve impulse, heartbeat, muscle contraction) consisting of a differential equation coupled with l slow and m fast equations. The slow [fast] equations correspond to subprocesses whose rates are slow [fast] relative to the rate of the primary phenomenon.
We develop a method of studying the principal, slow, and fast equations separately; piecing together the resulting solutions; and showing that these singular solutions correspond to true solutions of the system for certain parameter values.
