Relevant bibliographies by topics / Huxley Equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Huxley Equation'

Author: Grafiati
Published: 4 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Huxley Equation"

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Akkoyunlu, Canan. "FIFTH-ORDER COMPACT FINITE DIFFERENCE SCHEME FOR BURGERS-HUXLEY EQUATION." İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi 24, no. 47 (2025): 249–60. https://doi.org/10.55071/ticaretfbd.1627642.

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The Burgers-Huxley equation arises in several problems in science. The compact finite difference scheme (CFDS) has been developed for the Burgers-Huxley equation. This scheme has been compared different methods for the Burgers-Huxley equation. Dispersive properties are investigated for the linearized equations to examine the nonlinear dynamics after discretisation. The accuracy and computational efficiency of the compact finite differences scheme are shown in numerical test problems.
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İnan, B., and A. R. Bahadir. "Numerical solutions of the generalized Burgers-Huxley equation by implicit exponential finite difference method." Journal of Applied Mathematics, Statistics and Informatics 11, no. 2 (2015): 57–67. http://dx.doi.org/10.1515/jamsi-2015-0012.

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Abstract In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equations. Secondly, at each time-step Newton’s method is used to solve this nonlinear system then li
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El-Sayed El-Danaf, Talaat, Mfida Ali Zaki, and Wedad Moenaaem. "New numerical technique for solving the fractional Huxley equation." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 8 (2014): 1736–54. http://dx.doi.org/10.1108/hff-07-2013-0216.

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Purpose – The purpose of this paper is to investigate the possibility of extension to the variational iteration and the Adomian decomposition methods for solving nonlinear Huxley equation with time-fractional derivative. Design/methodology/approach – Objectives achieved the main methods: the fractional derivative of f (x) in the Caputo sense is first stated. Second, the time-fractional Huxley equation is written in a differential operator form where the differential operator is in Caputo sense. After acting on both sides by the inverse operator of the fractional differential operator in Caputo
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YOSHINAGA, TETSUYA, YASUHIKO SANO, and HIROSHI KAWAKAMI. "A METHOD TO CALCULATE BIFURCATIONS IN SYNAPTICALLY COUPLED HODGKIN–HUXLEY EQUATIONS." International Journal of Bifurcation and Chaos 09, no. 07 (1999): 1451–58. http://dx.doi.org/10.1142/s0218127499001000.

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We propose a numerical method for calculating bifurcations of periodic solutions observed in a model equation of Hodgkin–Huxley neurons coupled by excitatory synapses with a time delay. To illustrate the validity of the method, bifurcations in two-coupled Hodgkin–Huxley equations with variation of a coupling coefficient and time delay are studied.
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Ye, Feng, Xiaoting Zhang, Chunling Jiang, and Bo Zeng. "Comment on: "Solving the conformable Huxley equation using the complex method" [Electron. Res. Arch., 31 (2023), 1303–1322]." Electronic Research Archive 33, no. 1 (2025): 255–62. https://doi.org/10.3934/era.2025013.

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<p>Using the complex method, Guoqiang Dang and Qiyou Liu [Guoqiang Dang, Qiyou Liu, Electron. Res. Arch., 31 (2023), 1303–1322] have found some exact solutions of the conformable Huxley equation. In this comment, we first demonstrate that the elliptic function solutions and rational function solutions do not satisfy the complex conformable Huxley equation. Finally, all exact solutions of the conformable Huxley equation are given by us.</p>
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Broadbridge, P., B. H. Bradshaw, G. R. Fulford, and G. K. Aldis. "Huxley and Fisher equations for gene propagation: An exact solution." ANZIAM Journal 44, no. 1 (2002): 11–20. http://dx.doi.org/10.1017/s1446181100007860.

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AbstractThe derivation of gene-transport equations is re-examined. Fisher's assumptions for a sexually reproducing species lead to a Huxley reaction-diffusion equation, with cubic logistic source term for the gene frequency of a mutant advantageous recessive gene. Fisher's equation more accurately represents the spread of an advantaged mutant strain within an asexual species. When the total population density is not uniform, these reaction-diffusion equations take on an additional non-uniform convection term. Cubic source terms of the Huxley or Fitzhugh-Nagumo type allow special nonclassical s
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Sun, Yong-Li, Wen-Xiu Ma, Jian-Ping Yu, and Chaudry Masood Khalique. "Exact solutions of the Rosenau–Hyman equation, coupled KdV system and Burgers–Huxley equation using modified transformed rational function method." Modern Physics Letters B 32, no. 24 (2018): 1850282. http://dx.doi.org/10.1142/s0217984918502822.

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In this research, we study the exact solutions of the Rosenau–Hyman equation, the coupled KdV system and the Burgers–Huxley equation using modified transformed rational function method. In this paper, the simplest equation is the Bernoulli equation. We are not only obtain the exact solutions of the aforementioned equations and system but also give some geometric descriptions of obtained solutions. All can be illustrated vividly by the given graphs.
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Navickas, Zenonas, Minvydas Ragulskis, and Liepa Bikulčienė. "SPECIAL SOLUTIONS OF HUXLEY DIFFERENTIAL EQUATION." Mathematical Modelling and Analysis 16, no. 1 (2011): 248–59. http://dx.doi.org/10.3846/13926292.2011.579627.

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The conditions when solutions of Huxley equation can be expressed in special form and the procedure of finding exact solutions are presented in this paper. Huxley equation is an evolution equation that describes the nerve propagation in biology. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. It is shown that the solution produced by the Exp-function method may not hold for all initial conditions. It is proven that the analytical condition describing the existence of the produced solution in the space of initial conditions (or even in
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Zhou, Xin-Wei. "Exp-Function Method for Solving Huxley Equation." Mathematical Problems in Engineering 2008 (2008): 1–7. http://dx.doi.org/10.1155/2008/538489.

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Huxley equation is a core mathematical framework for modern biophysically based neural modeling. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. There are many methods to solve the equation, but each method can only lead to a special solution. This paper suggests a relatively new method called the Exp-function method for this purpose. The obtained result includes all solutions in open literature as special cases, and the generalized solution with some free parameters might imply some fascinating meanings hidden in Huxley equation.
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Inan, Bilge. "A New Numerical Scheme for the Generalized Huxley Equation." Bulletin of Mathematical Sciences and Applications 16 (August 2016): 105–11. http://dx.doi.org/10.18052/www.scipress.com/bmsa.16.105.

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In this paper, an implicit exponential finite difference method is applied to compute the numerical solutions of the nonlinear generalized Huxley equation. The numerical solutions obtained by the present method are compared with the exact solutions and obtained by other methods to show the efficiency of the method. The comparisons showed that proposed scheme is reliable, precise and convenient alternative method for solution of the generalized Huxley equation.
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Dissertations / Theses on the topic "Huxley Equation"

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Rameh, Raffael Bechara. "Aproximações dos modelos de Hodgkin-Huxley e FitzHugh-Nagumo usando equações diferenciais com atraso." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/8081.

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Submitted by Renata Lopes (renatasil82@gmail.com) on 2018-11-12T14:27:26Z No. of bitstreams: 1 raffaelbechararameh.pdf: 1503042 bytes, checksum: 87e66fa77937ca9a85aac3231b27ac84 (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-11-23T13:13:22Z (GMT) No. of bitstreams: 1 raffaelbechararameh.pdf: 1503042 bytes, checksum: 87e66fa77937ca9a85aac3231b27ac84 (MD5)<br>Made available in DSpace on 2018-11-23T13:13:22Z (GMT). No. of bitstreams: 1 raffaelbechararameh.pdf: 1503042 bytes, checksum: 87e66fa77937ca9a85aac3231b27ac84 (MD5) Previous issue date
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Attanayake, Champike. "Finite Elements and Practical Error Analysis of Huxley and EFK Equations." Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1215437536.

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Taylor, Gillian Clare. "Application of the Hodgkin-Huxley equations to the propagation of small graded potentials in neurons." Thesis, Heriot-Watt University, 1996. http://hdl.handle.net/10399/742.

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Zeng, Shangyou. "Spatial distribution and function of ion channels on neural axon." Ohio : Ohio University, 2005. http://www.ohiolink.edu/etd/view.cgi?ohiou1113855357.

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Schleimer, Jan Hendrik. "Spike statistics and coding properties of phase models." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2013. http://dx.doi.org/10.18452/16788.

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Ziel dieser Arbeit ist es eine Beziehung zwischen den biophysikalischen Eigenschaften der Nervenmembran, und den ausgeführten Berechnungen und Filtereigenschaften eines tonisch feuernden Neurons, unter Einbeziehen intrinsischer Fluktuationen, herzustellen. Zu diesem Zweck werden zu erst die mikroskopischen Fluktuationen, die durch das stochastische Öffnen und Schließen der Ionenkanäle verursacht werden, zu makroskopischer Varibilität in den Zeitpunkten des Auftretens der Aktionspotentiale übersetzt, denn es sind diese Spikezeiten die in vielen sensorischen Systemen informationstragenden sind
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Chen, Bo-Yun, and 陳博允. "Comparison of Hodgkin Huxley model and Poisson Nernst Planck equations." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/sw4uru.

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碩士<br>國立臺灣大學<br>應用數學科學研究所<br>107<br>This thesis presents a dynamic simulation of intracellular and extracellular ionic concentrations and electric potential, then create an action potential, which is generated by a difference of the electrochemical potential between two sides of a cell membrane. Ion species including Sodium, Potassium and Chlorine. This simulation would involve Poisson-Nernst-Planck (PNP) system and Hodgkin–Huxley (HH) model. The former gives a standard model for describing behaviors of ionic diffusion and electrophoresis. The latter gives a transformation between mechanism of
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Books on the topic "Huxley Equation"

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Royal Society (Great Britain). Discussion Meeting. Dynamical chaos: Proceedings of A Royal Society Discussion Meeting held on 4 and 5 February 1987. Princeton University Press, 1989.

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2

V, Berry Michael, Percival Ian 1931-, Weiss N. O, Royal Society (Great Britain), and British Academy, eds. Dynamical chaos: Proceedings of a Royal Society discussion meeting held on 4 and 5 February 1987. The Royal Society[and The British Academy], 1987.

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Royal Society (Great Britain). Discussion Meeting. Dynamical chaos: Proceedings of A Royal Society Discussion Meeting held on 4 and 5 February 1987. Princeton University Press, 1989.

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4

Koch, Christof. Biophysics of Computation. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195104912.001.0001.

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Neural network research often builds on the fiction that neurons are simple linear threshold units, completely neglecting the highly dynamic and complex nature of synapses, dendrites, and voltage-dependent ionic currents. Biophysics of Computation: Information Processing in Single Neurons challenges this notion, using richly detailed experimental and theoretical findings from cellular biophysics to explain the repertoire of computational functions available to single neurons. The author shows how individual nerve cells can multiply, integrate, or delay synaptic inputs and how information can b
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Williams, George C., and James Paradis. Evolution and Ethics: T.H. Huxley's Evolution and Ethics With New Essays on Its Victorian and Sociobiological Context. Princeton Univ Pr, 1989.

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Berry, Michael V., Ian C. Percival, and Nigel Oscar Weiss. Dynamical Chaos. Princeton University Press, 2017.

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Berry, Michael V., Ian C. Percival, and Nigel Oscar Weiss. Dynamical Chaos. Princeton University Press, 2014.

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Berry, Michael V., Ian C. Percival, and Nigel Oscar Weiss. Dynamical Chaos. Princeton University Press, 2014.

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Berry, Michael V., and I. C. Percival. Dynamical Chaos: Proceedings of a Royal Society Discussion Meeting Held on 4 and 5 February 1987. Princeton Univ Pr, 1989.

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Book chapters on the topic "Huxley Equation"

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Horgmo Jæger, Karoline, and Aslak Tveito. "The Cable Equation." In Differential Equations for Studies in Computational Electrophysiology. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_9.

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AbstractIn Chapter 6, we studied a simple version of the cable equation, where a diffusion term was added to the FitzHugh-Nagumo equations. In this chapter, we will revisit the cable equation and go through a simple derivation of the model. In addition, we will consider the numerical solution of the cable equation for a neuronal axon with membrane dynamics modeled by the Hodgkin-Huxley model.
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Appadu, Appanah Rao, Yusuf Olatunji Tijani, and Justin Munyakazi. "Computational Study of Some Numerical Methods for the Generalized Burgers-Huxley Equation." In Communications in Computer and Information Science. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4772-7_4.

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Omurtag, Ahmet. "Hodgkin-Huxley Equations." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_364.

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Ermentrout, G. Bard, and David H. Terman. "The Hodgkin–Huxley Equations." In Interdisciplinary Applied Mathematics. Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-87708-2_1.

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Courellis, Spiridon H., and Vasilis Z. Marmarelis. "Wiener Analysis of the Hodgkin-Huxley Equations." In Advanced Methods of Physiological System Modeling. Springer US, 1989. http://dx.doi.org/10.1007/978-1-4613-9789-2_16.

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Fitzgibbon, W., M. Parrott, and Y. You. "Global Dynamics of Singularly Perturbed Hodgkin-Huxley Equations." In Semigroups of Linear and Nonlinear Operations and Applications. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1888-0_8.

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Arrigo, P., L. Marconi, G. Morgavi, S. Ridella, C. Rolando, and F. Scalia. "High Sensitivity Chaotic Behaviour in Sinusoidally Driven Hodgkin-Huxley Equations." In Chaos in Biological Systems. Springer US, 1987. http://dx.doi.org/10.1007/978-1-4757-9631-5_14.

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Hearne, P. G., S. Manchanda, M. Janahmadi, et al. "Solutions to Hodgkin-Huxley Equations: Functional Analysis of a Molluscan Neurone." In Computation in Neurons and Neural Systems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4615-2714-5_1.

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Tanaka, Hiroaki, and Kazuyuki Aihara. "Chaotic behavior of the Hodgikin-Huxley equations under small random noise." In Complexity and Diversity. Springer Japan, 1997. http://dx.doi.org/10.1007/978-4-431-66862-6_35.

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Hirose, Akira. "Two-dimensional Hodgkin-Huxley equations for investigating a basis of pulse-processing neural networks." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0020137.

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Conference papers on the topic "Huxley Equation"

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Kushner, Alexei G., and Ruslan I. Matviychuk. "Finite Dimensional Dynamics and Exact Solutions of Burgers – Huxley Equation." In 2019 Twelfth International Conference "Management of large-scale system development" (MLSD). IEEE, 2019. http://dx.doi.org/10.1109/mlsd.2019.8910973.

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Appadu, Appanah Rao, Bilge İnan, and Tijani Yusuf Olatunji. "Comparison of some numerical methods for the Burgers-Huxley equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026501.

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Tomar, Amit, Jahanvi, Antim Chauhan, and Anu Rani. "Approximate analytical solution of coupled burgers and Burgers Huxley equation by RDTM." In INTERNATIONAL CONFERENCE ON ADVANCES IN PURE & APPLIED MATHEMATICS (ICAPAM). AIP Publishing, 2025. https://doi.org/10.1063/5.0265065.

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Appadu, Appanah Rao, and Yusuf Olatunji Tijani. "On the numerical solution of 2D Burgers-Huxley equation using NSFD and classical methods." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081374.

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Li, Yali, and N. C. Goulbourne. "Electro-Chemo-Mechanical Modeling of the Artery Myogenic Transient and Steady-State Response." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-39237.

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Active contraction of smooth muscle results in the myogenic response and vasomotion of arteries, which adjusts the blood flow and nutrient supply of the organism. It is a multiphysic process coupled electrical and chemical kinetics with mechanical behavior of the smooth muscle. This paper presents a new constitutive model for the media layer of the artery wall to describe the myogenic response of artery wall for different transmural pressures. The model includes two major components: electrobiochemical, and chemomechanical parts. The electrochemical model is a lumped Hodgkin-Huxley-type cell m
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Kameneva, Tatiana, Hamish Meffin, Anthony N. Burkitt, and David B. Grayden. "Bistability in Hodgkin-Huxley-type equations." In 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, 2018. http://dx.doi.org/10.1109/embc.2018.8513233.

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Repperger, D. W., C. A. Phillips, and A. Neidhard. "A study on stochastic resonance involving the Hodgkin-Huxley equations." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.945547.

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Rababah, Abedallah. "Numerical solution of Burger-Huxley second order partial differential equations using splines." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027712.

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Kako, Najdavan A., Adnan M. Abdulazeez, and Haval T. Sadeeq. "Effect of Colored Noise on Neuron Membrane Size Using Stochastic Hodgkin-Huxley Equations." In 2021 7th International Engineering Conference “Research & Innovation amid Global Pandemic" (IEC). IEEE, 2021. http://dx.doi.org/10.1109/iec52205.2021.9476110.

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Zlotnik, Anatoly, and Jr-Shin Li. "Optimal Asymptotic Entrainment of Phase-Reduced Oscillators." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-5923.

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We derive optimal periodic controls for entrainment of a self-driven oscillator to a desired frequency. The alternative objectives of minimizing power and maximizing frequency range of entrainment are considered. A state space representation of the oscillator is reduced to a linearized phase model, and the optimal periodic control is computed from the phase response curve using formal averaging and the calculus of variations. Computational methods are used to calculate the periodic orbit and the phase response curve, and a numerical method for approximating the optimal controls is introduced.
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