Regulating spatiotemporal dynamics for a delay Gierer–Meinhardt model
Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Cited by 2 publications
References 45 publications
Steady-states of the Gierer–Meinhardt system in exterior domains
We discuss the existence and nonexistence of solutions to the steady-state Gierer–Meinhardt system { − Δ u = u p v q + λ ρ ( x ) , u > 0 in ℝ N ∖ K , − Δ v = u m v s , v > 0 in ℝ N ∖ K , ∂ u ∂ ν = ∂ v ∂ ν = 0 on ∂ K , u ( x ) , v ( x ) → 0 as | x | → ∞ , where K ⊂ R N ( N ⩾ 2 ) is a compact set, ρ ∈ C loc 0 , γ ( R N ∖ K ― ) , γ ∈ ( 0 , 1 ) , is a nonnegative function and p , q , m , s , λ > 0 . Combining fixed point arguments with suitable barrier functions, we construct solutions with a prescribed asymptotic growth at infinity. Our approach can be extended to many other classes of semilinear elliptic systems with various sign of exponents.
Steady-states of the Gierer–Meinhardt system in exterior domains
We discuss the existence and nonexistence of solutions to the steady-state Gierer–Meinhardt system { − Δ u = u p v q + λ ρ ( x ) , u > 0 in ℝ N ∖ K , − Δ v = u m v s , v > 0 in ℝ N ∖ K , ∂ u ∂ ν = ∂ v ∂ ν = 0 on ∂ K , u ( x ) , v ( x ) → 0 as | x | → ∞ , where K ⊂ R N ( N ⩾ 2 ) is a compact set, ρ ∈ C loc 0 , γ ( R N ∖ K ― ) , γ ∈ ( 0 , 1 ) , is a nonnegative function and p , q , m , s , λ > 0 . Combining fixed point arguments with suitable barrier functions, we construct solutions with a prescribed asymptotic growth at infinity. Our approach can be extended to many other classes of semilinear elliptic systems with various sign of exponents.
A new chemical networked system: spatial-temporal evolution and control
This paper constructs a scale-free chemical network based on the Gierer-Meinhardt (GM) system and investigates its Turing instability. We establish a fractional-order single-node GM system with delay and design a fractional-order proportional derivative (PD) control strategy for the issue of bifurcation control. Using delay as bifurcation parameter, the existence of Hopf bifurcation is proven, and control over bifurcation threshold points is achieved through a fractional-order PD control strategy. For the scale-free chemical network based on the GM system, we obtain the condition of how the Turing instability occurs. We derive how the number of edges for the new nodes changes the stability of the network-organized system and investigate the relationship between degrees of nodes and eigenvalues of the network matrix. We give the instability condition caused by diffusion in the network-organized system. Finally, the numerical simulations verify analytical results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
Contact Info
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Product
Resources
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.
