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Cusp catastrophe in a bistable perception energy model with additive and parametric noise

Lev Ryashko, Alexander Pisarchik, Irina Bashkirtseva
Using the cusp catastrophe theory formalism we analyze stochastic sensitivity of a bistable energy model, often used for description of visual perception, subject to both additive and parametric noise. In perception psychology, different kinds of noise may be associated with inherent brain noise originated from physiological processes and random synaptic connections of brain neurons due to interactions among neural networks.
We demonstrate that parametric noise leads to the total suppression of oscillations when the system stays in an unstable equilibrium, whereas in the presence of additive noise the oscillations still exist, but strongly suppressed. Using a new approach based on the stochastic sensitivity function and the method of confidence intervals we demonstrate the effect of noise on the range of hysteresis observed in bistable perception when a control parameter is changed. This approach allows prediction of the hysteresis squeezing when the intensity of additive noise is increased. Stochastic bifurcations associated with transformation of the system from bistable to monostable are studied using probability density functions.
CYBERNETICS AND PHYSICS, Vol. 6, No. 3. 2017, 131–138
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