Controlling Spiral Waves in a Model of Two-Dimensional Arrays of Chua's Circuits

Hu, Gang; Xiao, Jinghua; Chua, Leon O.; Pivka, Ladislav

doi:10.1103/physrevlett.80.1884

Cited by 47 publications

(19 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[6]–[8], [38]. We model this myocyte-fibroblast bilayer by using the following discrete equations [39], [40]: here the dots above and denote time derivatives, and represent, respectively, intercellular couplings in the myocyte and fibroblast layers; and and account for cross couplings between myocyte and fibroblast layers; if one of the cross-coupling coefficients, say , is nonzero, then the other, , must also be nonzero to ensure current conservation; myocyte and fibroblast composites are coupled at a given site by ; in addition, we allow for intercellular couplings (see Fig. S1 in Material S1) that can be categorized naturally as follows: (A) zero-sided: ; (B) one-sided: ; and (C) two-sided: ; the index () refers to the cell associated with the node under consideration; the conductances , and are in nS.…”

Section: Model and Methodsmentioning

confidence: 99%

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

et al. 2013

View full text Add to dashboard Cite

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

show abstract

Section: Model and Methodsmentioning

confidence: 99%

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

et al. 2013

View full text Add to dashboard Cite

show abstract

“…5(c)). This 'local strategy' has the important meaning for the control scheme on networks (control process has been an attractive topic to many research groups [17,18,19,20], but controlling networks is not such an explored field yet) and reflects the self-structuring nature of the autocatalytic network.…”

Section: Emergence Of Communitiesmentioning

confidence: 99%

Spatio-temporal dynamics in the origin of genetic information

Kim

Jeong

2005

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

We study evolutionary processes induced by spatio-temporal dynamics in prebiotic evolution. Using numerical simulations we demonstrate that hypercycles emerge from complex interaction structures in multispecies systems. In this work we also find that 'hypercycle hybrid' protects the hypercycle from its environment during the growth process. There is little selective advantage for one hypercycle to maintain coexistence with others. This brings the possibility of the outcompetition between hypercycles resulting in the negative effect on information diversity. To enrich the information in hypercycles, symbiosis with parasites is suggested. It is shown that symbiosis with parasites can play an important role in the prebiotic immunology.

show abstract

“…They display many drift behaviors with different external fields, i.e., illumination [8], electric fields [9–14], and magnetic fields [15]. In particular, under external forcing by periodic light pulses and feedback-controlled sequences of light pulses, spiral wave entrainment and resonance can be observed [16,17].…”

Section: Introductionmentioning

confidence: 99%

Resonance drifts of spiral waves on media of periodic excitability

et al. 2012

Phys. Rev. E

View full text Add to dashboard Cite

Spiral waves subjected to an external periodic force exhibit very rich spatiotemporal dynamics including resonance attractors. In previous research, the modulation was mainly described as additional induced flow in the system, and a theory has been developed based on reducing the spiral wave dynamics to a low-dimensional map. In this paper, another perspective for study of the resonance attractors is suggested. The periodic modulation of excitability is directly described by the time dependence of the parameters. This approach gives us nice results that are well consistent with the experiments. Additionally, when we force the spiral with a frequency larger than its intrinsic frequency, another branch of spiral meandering with qualitatively different properties is observed. Full resonances are also clearly indicated. Furthermore, a kinetic model for spiral movement suggested in our previous paper is applied to this case. The theoretical results are in good quantitative agreement with numerical simulations. The model could be widely used in different excitable systems.

show abstract

Controlling Spiral Waves in a Model of Two-Dimensional Arrays of Chua's Circuits

Cited by 47 publications

References 16 publications

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Spatio-temporal dynamics in the origin of genetic information

Resonance drifts of spiral waves on media of periodic excitability

Contact Info

Product

Resources

About