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Article
Mathematics, Applied
Mengxin Chen et al.
Summary: This paper investigates the species interaction model with the ratio-dependent Holling III functional response and strong Allee effect. The existence and non-existence of steady states, temporal bifurcation, and the boundedness of global positive solutions are explored. Results on the upper and lower bounds of positive solutions for the associated elliptic system are provided. The impact of the ratio-dependent Holling III functional response and strong Allee effect on the dynamical behaviors of the species interaction systems is illustrated through numerical simulations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
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Mengxin Chen et al.
Summary: The paper introduces and investigates a depletion-type reaction-diffusion Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme and homogeneous Neumann boundary conditions. It provides theoretical analysis and numerical simulations to explore stability, existence, and bifurcation properties in the model. The results confirm the theoretical findings and provide additional insights through numerical simulations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Interdisciplinary Applications
Mengxin Chen et al.
Summary: This paper investigates the Leslie-Gower type predator-prey system with the ratio-dependent Holling III functional response and Neumann boundary conditions. The existence of the codimension-two Turing-Hopf point is identified, and amplitude equations are derived using weakly nonlinear analysis to explore the spatiotemporal dynamics near the C2THP. The temporal patterns, hexagonal patterns, and plane wave patterns can be presented through amplitude equations, along with the sufficient conditions of their existence and stability.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Nikos I. Kavallaris et al.
Summary: The paper aims to study the dynamics of the shadow system of a Gierer-Meinhardt model, focusing on deriving blow-up results for its non-local equation. It investigates the diffusion-driven instability patterns and stable patterns near constant stationary solutions, with theoretical results verified numerically and a numerical approach used when analytical methods fail.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Chemistry, Multidisciplinary
Xiaoxue Fu et al.
Summary: By analyzing the amplitude equations, complex dynamics such as nonconstant steady state solutions, spatially homogeneous periodic solutions and spatially inhomogeneous periodic solutions near the Turing-Hopf bifurcation point are discovered. The codimension-two Turing-Hopf bifurcation can induce more complex patterns compared to codimension-one Turing instability or Hopf bifurcation, such as spatially inhomogeneous periodic solutions, which can explain spatiotemporal resonance phenomena between activators and inhibitors in chemical reactions. Theoretical analysis is verified through numerical simulations presenting different bifurcation solutions corresponding to different regions near the bifurcation point of the Brusselator model.
JOURNAL OF MATHEMATICAL CHEMISTRY
(2021)
Article
Chemistry, Multidisciplinary
Andrea Cassani et al.
Summary: Chemical oscillators are open systems exhibiting periodic variations in reaction species concentration due to complex physico-chemical phenomena, leading to bistability, limit cycle attractors, spiral waves, Turing patterns, and deterministic chaos. The Belousov-Zhabotinsky reaction serves as a notable example of non-linear behavior in chemical systems, occurring in homogenous media and offering insights into more complex deriving phenomena. Models of Belousov-Zhabotinsky-type reactions under different operating conditions have been studied, focusing on stability and complex behaviors as a function of bifurcation parameters. Mathematically explaining the rise of waves and fronts, as well as the birth and evolution of chaotic ODEs system, provides valuable information for future biochemical reactions and reactor designs.
JOURNAL OF MATHEMATICAL CHEMISTRY
(2021)
Article
Mathematics, Interdisciplinary Applications
J. Sarria-Gonzalez et al.
Summary: Strong Turing-Hopf instabilities in the Lengyel-Epstein CIMA reaction-diffusion model can lead to time periodic spatially inhomogeneous solutions induced by diffusive instability of the spatially homogeneous limit cycle. Numerical simulations confirmed theoretical results by showing the formation of twinkling patterns under certain parameter values.
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(2021)
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T. Bansagi et al.
Article
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H. Merdan et al.
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(2015)
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Jiayin Jin et al.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2013)
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E Freire et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2005)
