Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Abstract

A mathematical model of the biochemical reaction with nonlinear recycling of the product into substrate is considered. The main control parameter of this model is the substrate injection rate, which is subject to random disturbances. We study noise-induced oscillations in the parameter zones where the system is bistable and exhibit a coexistence of the equilibrium and limit cycle, or two stable cycles (birhythmicity). Phenomena of the generation of noisy birhythmicity and 'stochastic preference' of attractors are studied on the basis of the stochastic sensitivity function technique, confidence domains method, and statistics of interspike intervals.

Using entropy-driven amplifier circuit response to build nonlinear model under the influence of Lévy jump

“…Many nonlinear system modeling methods [ 23 – 28 ] have been proposed. Based on the above methods, nonlinear system models can be established [ 29 , 30 ], and sensitivity analysis [ 31 , 32 ], stability analysis [ 30 , 33 , 34 ] and bifurcation analysis [ 35 – 37 ] can be performed on them. A parametric model of dosetime response is proposed in [ 38 ], demonstrating the effectiveness of our model for all available anticancer compounds.…”

Multistability and Stochastic Dynamics of Rulkov Neurons Coupled Via a Chemical Synapse

“…The interplay between nonlinearity and stochasticity, especially in the presence of multistability, gives rise to a wide range of interesting effects, such as noise-induced transitions [29,30], stochastic and coherent resonances [31][32][33], noiseinduced bifurcations [34] and chaos [35][36][37], and stochastic excitability [38]. Currently, in the study of these effects, along with the traditionally widely used but very costly methods of direct numerical simulation, an analytical approach based on the technique of stochastic sensitivity functions is being actively developed [39,40]. A parametric description of the stochastic sensitivity of attractors makes it possible to construct an efficient approximation of the corresponding noisegenerated probability distributions in the form of confidence domains.…”