Stability analysis for Selkov-Schnakenberg reaction-diffusion system
K.S. Al Noufaey
Abstract
Abstract This study provides semi-analytical solutions to the Selkov-Schnakenberg reaction-diffusion system. The Galerkin method is applied to approximate the system of partial differential equations by a system of ordinary differential equations. The steady states of the system and the limit cycle solutions are delineated using bifurcation diagram analysis. The influence of the diffusion coefficients as they change, on the system stability is examined. Near the Hopf bifurcation point, the asymptotic analysis is developed for the oscillatory solution. The semi-analytical model solutions agree accurately with the numerical results.
Topics & Concepts
MathematicsOrdinary differential equationHopf bifurcationBifurcation diagramReaction–diffusion systemGalerkin methodPartial differential equationMathematical analysisLimit cycleBifurcationStability (learning theory)Differential equationLimit (mathematics)Finite element methodPhysicsThermodynamicsNonlinear systemMachine learningComputer scienceQuantum mechanicsNonlinear Dynamics and Pattern FormationFractional Differential Equations SolutionsNumerical methods for differential equations