Abstract
Nonlinear system of molecular self-replication is modeled with stochastic considerations. External noise is introduced through the fluctuating replication rate parameter. Treatment with white noise formulation basing on Stratonovich interpretation, together with approximation schemes enable us to derive the steady state as well as transient characteristics of the system. Transient processes near a noise-induced instability are found to exhibit critical slowing-down and attraction-basin shrinkage. The role played by the nonlinearity of system is discussed. Nonlinear relaxation times defined in terms of the first two moments are computed numerically, so that comparison can be made between them and the actual relaxation time.
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