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Turing–Turing bifurcation in an activator–inhibitor system with gene expression time delay
Communications in Nonlinear Science and Numerical SimulationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Transition from Amplitude to Oscillation Death via Turing Bifurcation
Physical Review Letters, 2013Coupled oscillators are shown to experience two structurally different oscillation quenching types: amplitude death (AD) and oscillation death (OD). We demonstrate that both AD and OD can occur in one system and find that the transition between them underlies a classical, Turing-type bifurcation, providing a clear classification of these significantly ...
Koseska, A., Volkov, E., Kurths, J.
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TURING BIFURCATION IN A HUMAN MIGRATION MODEL OF SCHEURLE–SEYDEL TYPE
International Journal of Bifurcation and Chaos, 2013The main goal of this paper is to continue the investigations of the important system proposed by [Scheurle & Seydel, 2000] and modified by [Sándor, 2003]. I consider spatio-temporal models for the behavior of students in graduate programs at neighboring universities as systems of ODE which describe two-identical patch-two-species systems linked ...
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Spatial resonance and Turing–Hopf bifurcations in the Gierer–Meinhardt model
Nonlinear Analysis: Real World Applications, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Rui, Song, Yongli
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Bifurcation and Turing patterns of reaction–diffusion activator–inhibitor model
Physica A: Statistical Mechanics and its Applications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Ranchao +3 more
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Turing-Hopf bifurcation analysis in a superdiffusive predator-prey model
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018The predator-prey model with superdiffusion is investigated in this paper. Here, the existence of Turing-Hopf bifurcation and the resulting dynamics are studied. To understand such a degenerate bifurcation in the anomalously diffusive system, the weakly nonlinear analysis is employed and the amplitude equations at the Turing-Hopf bifurcation point are ...
Biao Liu, Ranchao Wu, Liping Chen
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Turing bifurcations with a temporally varying diffusion coefficient
Journal of Mathematical Biology, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Normal form of Turing–Turing bifurcation for the diffusive Bazykin system with prey-taxis
International Journal of BiomathematicsIn this paper, we introduce prey-taxis to the diffusive Bazykin system and study the codimension-two Turing–Turing bifurcation of this modified system. For the local system, i.e. without diffusion terms and the prey-taxis term, we investigate the stability of the unique positive equilibrium.
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On the convective nature of the instability of a front undergoing a supercritical Turing bifurcation
Mathematics and Computers in Simulation, 2009The author studies some stability questions related to the parabolic system \[ \begin{aligned} & \partial_tu_1=\partial^2_xu_1+\tfrac12(u_1-c)(1-u^2)+\gamma_1u^2_2\\ & \partial_tu_2=-(1+\partial^2_x)^2u_2+\alpha u_2-u^3_2-\gamma_2u_2(1+u_1)\end{aligned}\tag{1} \] already considered in [(*) \textit{A. Ghazaryan} and \textit{B. Sandstede}, SIAM J.
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