Selkov glycolytic model with diffusion: Patterns, multistability, and stochastic transitions

Abstract

We consider a distributed variant of the Selkov mathematical model of glycolysis with diffusion and stochastic disturbances. The Turing instability zone, in which nonhomogeneous patterns are formed, is determined parametrically. Diversity of waveform spatial structures with different number of peaks is described and studied depending on the diffusion coefficients. The coexistence of various patterns of different waveforms and amplitudes is demonstrated. The quantitative analysis of the pattern formation from the random initial states is carried out using statistics and harmonic coefficients. Multistage noise-induced transitions between coexisting spatial structures are discussed.

Noise-induced formation of heterogeneous patterns in the Turing stability zones of diffusion systems

“…where D * u corresponds to the Turing bifurcation [25]. In this paper, we fix D v = 0.001, ϑ = 1, and L = 1.…”

“…models attracts attention of many researchers [16][17][18][19][20][21]. In these studies, a spatial version of the Selkov model [22] is actively used [23][24][25][26]. Note that even the local version of the Selkov model shows interesting effects of oscillatory behavior in glycolysis [27][28][29][30], including those under the influence of stochastic perturbations [31,32].…”

“…Noise-induced phenomena in various systems with diffusion are widely studied [33][34][35][36][37][38]. The influence of noise on the processes of pattern formation in zones of Turing instability of spatial glycolytic models is subject of research investigations [25,39]. Now, of particular interest is the question of whether noise can play a constructive role in the process of pattern formation in the Turing stability zone, where homogeneous equilibrium is the only attractor.…”

Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique

“…At present, an urgent problem in the theory of self-organization is the study of the influence of random perturbations on the processes of generation and transformation of spatial structures [17][18][19][20][21][22][23]. These investigations may reveal new phenomena, even in well-studied deterministic models, exposing them from a new perspective.…”