We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular fo...We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular for the excitable media with equal diffusion, we obtain a close system for the motion of the filament. With an example of the Oregonator model, our results are in good agreement with those simulated by Winfree.展开更多
In this paper, by making use of Duan＇s topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the lim...In this paper, by making use of Duan＇s topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z（x, t）. [t is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes （splitting, merging, or encountering） during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the ＂exclusion principle＂ in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the ＂exclusion principle＂ is also protected by topology.展开更多
The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear...The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments.展开更多
This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by construc...This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.展开更多
In this paper we introduce a new mathematical model for the active contraction of cardiac muscle,featuring different thermo-electric and nonlinear conductivity properties.The passive hyperelastic response of the tissu...In this paper we introduce a new mathematical model for the active contraction of cardiac muscle,featuring different thermo-electric and nonlinear conductivity properties.The passive hyperelastic response of the tissue is described by an orthotropic exponential model,whereas the ionic activity dictates active contraction in-corporated through the concept of orthotropic active strain.We use a fully incompressible formulation,and the generated strain modifies directly the conductivity mechanisms in the medium through the pull-back transformation.We also investigate the influence of thermo-electric effects in the onset of multiphysics emergent spatiotem-poral dynamics,using nonlinear diffusion.It turns out that these ingredients have a key role in reproducing pathological chaotic dynamics such as ventricular fibrillation during inflammatory events,for instance.The specific structure of the governing equations suggests to cast the problem in mixed-primal form and we write it in terms of Kirchhoff stress,displacements,solid pressure,dimensionless electric potential,activation generation,and ionic variables.We also advance a new mixed-primal finite element method for its numerical approximation,and we use it to explore the properties of the model and to assess the importance of coupling terms,by means of a few computational experiments in 3D.展开更多
文摘We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular for the excitable media with equal diffusion, we obtain a close system for the motion of the filament. With an example of the Oregonator model, our results are in good agreement with those simulated by Winfree.
基金Supported by the National Natural Science Foundation of China under Grant No.10275030the Cuiying Programm of Lanzhou University under Grant No.22500-582404
文摘In this paper, by making use of Duan＇s topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z（x, t）. [t is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes （splitting, merging, or encountering） during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the ＂exclusion principle＂ in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the ＂exclusion principle＂ is also protected by topology.
文摘The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60572073 and 60871025)the Natural Science Foundation of Guangdong Province,China (Grant Nos 8151009001000060,5001818 and 8351009001000002)
文摘This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.
基金supported by the Engineering and Physical Sciences Research Council(EPSRC)through the research grant EP/R00207X。
文摘In this paper we introduce a new mathematical model for the active contraction of cardiac muscle,featuring different thermo-electric and nonlinear conductivity properties.The passive hyperelastic response of the tissue is described by an orthotropic exponential model,whereas the ionic activity dictates active contraction in-corporated through the concept of orthotropic active strain.We use a fully incompressible formulation,and the generated strain modifies directly the conductivity mechanisms in the medium through the pull-back transformation.We also investigate the influence of thermo-electric effects in the onset of multiphysics emergent spatiotem-poral dynamics,using nonlinear diffusion.It turns out that these ingredients have a key role in reproducing pathological chaotic dynamics such as ventricular fibrillation during inflammatory events,for instance.The specific structure of the governing equations suggests to cast the problem in mixed-primal form and we write it in terms of Kirchhoff stress,displacements,solid pressure,dimensionless electric potential,activation generation,and ionic variables.We also advance a new mixed-primal finite element method for its numerical approximation,and we use it to explore the properties of the model and to assess the importance of coupling terms,by means of a few computational experiments in 3D.
