scholarly journals Propagation dynamics of a time periodic and delayed reaction-diffusion model without quasi-monotonicity

2019 ◽  
Vol 372 (3) ◽  
pp. 1751-1782 ◽  
Author(s):  
Liang Zhang ◽  
Zhi-Cheng Wang ◽  
Xiao-Qiang Zhao
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Reaction Diffusion Model ◽  
Propagation Dynamics ◽  
Time Periodic

scholarly journals TRAVELING WAVE SOLUTIONS IN A STAGE-STRUCTURED DELAYED REACTION-DIFFUSION MODEL WITH ADVECTION

2015 ◽  
Vol 20 (2) ◽  
pp. 168-187
Author(s):  
Liang Zhang ◽  
Huiyan Zhao
Keyword(s):  
Diffusion Model ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Delayed Reaction ◽  
Wave Solutions ◽  
Reaction Diffusion Model ◽  
Travelling Fronts ◽  
Appl Math

We investigate a stage-structured delayed reaction-diffusion model with advection that describes competition between two mature species in water flow. Time delays are incorporated to measure the time lengths from birth to maturity of the populations. We show there exists a finite positive number c∗ that can be characterized as the slowest spreading speed of traveling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium. The model and mathematical result in [J.F.M. Al-Omari, S.A. Gourley, Stability and travelling fronts in Lotka–Volterra competition models with stage structure, SIAM J. Appl. Math. 63 (2003) 2063–2086] are generalized.

Bifurcations in Twinkling Patterns for the Lengyel–Epstein Reaction–Diffusion Model

2021 ◽  
Vol 31 (11) ◽  
pp. 2150164
Author(s):  
J. Sarría-González ◽  
Ivonne Sgura ◽  
M. R. Ricard
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Diffusion Model ◽  
Reaction System ◽  
Reaction Diffusion ◽  
Spatially Inhomogeneous ◽  
Reaction Diffusion Model ◽  
Spatially Homogeneous ◽  
Time Periodic ◽  
Theoretical Results

Conditions for the emergence of strong Turing–Hopf instabilities in the Lengyel–Epstein CIMA reaction–diffusion model are found. Under these conditions, time periodic spatially inhomogeneous solutions can be induced by diffusive instability of the spatially homogeneous limit cycle emerging at a supercritical Bautin–Hopf bifurcation about the unstable steady state of the reaction system. We report numerical simulations by an Alternating Directions Implicit (ADI) method that show the formation of twinkling patterns for a chosen parameter value, thus confirming our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document