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Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
where g(q>) = - sin(q> - a) + r sin(2q>) is coupling strength function, i = 1, . . . , 3, j = 0, 1.
Thus, the ensemble consists of two groups of three oscillators, the oscillators within the group connected with coupling coefficient equal 1 and oscillators of the various groups - with coupling coefficient £. This ensemble demonstrates chimeric state in which one part of the oscillators is synchronized in frequency, and the other part of the oscillators - no. Each active node in the wireless network is implemented as a pair of ultra-wideband wireless transceiver and the connected actuator. The actuator is a card equipped with a microcontroller, as a calculating device, and multicolor LEDs as a visualization tool. To simulate an ensemble of coupled oscillators, each oscillator in the experiments of the ensemble is associated with a node is an active network. The equation of the oscillator are integrated on the microcontroller, the communication between the oscillators are realized through wireless channels, and the oscillator phase is visualized by means of colored LEDs. This approach allows an arbitrary network topology and a visual demonstration of dynamic patterns of the ensemble.
The report examines the technique of modeling with the help of the active wireless network, the experimental results of the observation of different dynamic regimes of the ensemble and their analysis. The study was performed by a grant from the Russian Science Foundation (Project № 16-19-00084)
References
1. Kuramoto Y. Chemical oscillations, waves and turbulence. Berlin : Springer-Verlag. 1984.
2. Dmitriev A. S., Yemelyanov R. Yu., Gerasimov M. Yu., Itskov V. V. Active ultra wideband wireless networks usage for modelling ensembles of nonlinear continuous time dynamical systems //Nonlinear phenomena in complex systems. 2015. V. 18. №. 4. P. 456-466.
3. Ashwin P., Burylko O. Weak chimeras in minimal networks of coupled phase oscillators //Chaos: An Interdisciplinary Journal of Nonlinear Science. 2015. V. 25. №. 1. P. 013106.
On the Dynamics of Some Small Hypercycles with Short-Circuits
Josep Sardanyés1, J. Tomás Lazaro2*, Toni Guillamon3, and Ernest Fontich4
1 ICREA-Complex Systems Lab, Universitat Pompeu Fabra and Institut de Biología Evolutiva CSIC-UPF, Barcelona, Spain;
2 Departament de Matemàtiques Universitat Politécnica de Catalunya and Barcelona Graduate School of Mathematics BGSMath, Barcelona, Spain;
3 Departament de Matemàtiques Universitat Politécnica de Catalunya and Barcelona Graduate School of Mathematics BGSMath, Barcelona, Spain;
4 Departament de Matemàtiques i Informática Universitat de Barcelona and Barcelona Graduate School of Mathematics BGSMath, Barcelona, Spain.
* Presenting e-mail: jose.tomas.lazaro@upc.edu
It is known that hypercycles are sensitive to the so-called parasites and short-circuits. While the impact of parasites has been widely investigated for well-mixed and spatial hypercycles, the effect of short-circuits in hypercycles remains poorly understood. In this talk we will present, briefly, a description of the mean field and spatial dynamics of two small, asymmetric hypercycles with short-circuits: first, we consider a 2-member hypercycle with one of the species containing an autocatalytic loop, which represents the simplest case with a short-circuit; second, we add a third species which closes the 3-member hypercycle and preserving the initial autocatalytic short-circuit and the 2-member inner cycle. We characterize the bifurcations and transitions involved in the dominance of the short-circuits and in hypercycles' size. The spatial simulations reveal a random-like and mixed distribution of the hypercycle species in the all-species coexistence scenario, ruling out the presence of large-scale spatial patterns such as spirals or spots typical of larger hypercycles. MonteCarlo simulations reveal a drastic decrease of the probability of finding stable hypercycles with short-circuits when passing from the 2-member to the 3-member scenario.
Acknowledgements
We want to thank Ricard Solé and José Antonio Darós for their comments and fruitful discussions. This work has been partially funded by the Botín Foundation, by Banco Santander through its Santander Universities Global Division (JS); the Spanish grants MINECO MTM2013-41168-P (EF), MTM2015-71509-C2-2-R (TG) and MTM2015-65715-P (JTL); the Catalan grants AGAUR 2014SGR-1145 (EF) and 2014SGR-504 (TG, JTL); the grant 14-41-00044 of RSF at the Lobachevsky University of Nizhny Novgorod (Russia) (JTL); and the European Marie Curie Action FP7-PEOPLE-2012-IRSES: BREUDS (JTL).
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Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
References
1. Kauffman, Press Oxford University, 1993.
2. P. Eigen, M. Schuster, Springer-Verlag, 1979.
3. M. Eigen, J. McCaskill, and P. Schuster, J. Phys. Chem., 1988, 92(1), 6881-6891.
4. P. Boerlijst, M.C. Hogeweg, Phys. D Nonlinear Phenom., 1991, 48, 17-28.
5. Pan-Jun Kim and Hawoong Jeong, Phys. D, 2005, 203, 88-99.
6. J. Sardanyés and R. Solé, J. Theor. Biol., 2006, 243(4), 468-482.
7.M.B. Cronhjort, Phys. D, 1997, 101, 289-298.
Mechanical and Electrical Oscillations and Their Role in Sensory Hair Cells
A.B. Neiman1 * and R.M. Amro2
1 Department of Physics & Astronomy and Neuroscience Program, Ohio University, Athens, Ohio, USA;
2 Department of Physics & Astronomy, Ohio University, Athens, Ohio, USA. * Presenting e-mail: neimana@ohio.edu
Background
Hair cells are mechanoreceptors which transduce mechanical vibrations to electrical signals in peripheral organs of senses of hearing and balance in vertebrates. Somatic cell motility and active motility of the hair bundle, mechanically sensitive structure on the hair cell apex, are two main mechanisms by which hair cells can amplify mechanical stimuli. In amphibians and some reptiles active processes in hair cells result in noisy mechanical oscillation of hair bundles, which may lead to frequency selective amplification. The same cells often demonstrate spontaneous electrical oscillation of their somatic potentials, a signature of yet another amplification mechanism. Functional role of voltage oscillation is not well understood.
Aims and Methods
We use computational modeling to address the following questions: (i) how the interaction of two distinct unequally noisy oscillators, mechanical and electrical, embedded in the hair cell, affect its spontaneous dynamics; (ii) how synchronous oscillatory activity helps to battle inevitable noise, and (iii) shapes sensitivity of amphibian hair cells to external mechanical signals. The model employs a Hodgkin-Huxley-type system for the basolateral electrical compartment [1] and a nonlinear hair bundle oscillator for the mechanical compartment [2], which are coupled bidirec-tionally. In the model, forward coupling is provided by the mechanoelectrical transduction current, flowing from the hair bundle to the cell soma. Backward coupling is due to reverse electromechanical transduction, whereby variations of the membrane potential affect adaptation processes in the hair bundle.
Conclusions
Despite noise, the stochastic hair bundle oscillations can be synchronized by external periodic force of few pN amplitude in a finite range of control parameters of the model. Furthermore, the hair bundle oscillations can be synchronized by oscillating receptor voltage [3]. Electrical and mechanical self-oscillations can result from bidirectional coupling [4], and their coherence of can be maximized by tuning the coupling strengths [4,5]. Consistent with previous experimental work [6], the model demonstrates that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels [4]. We show that sensitivity of the hair cell to weak mechanical stimuli can be maximized by varying coupling strengths, and that stochasticity of the hair bundle compartment is a limiting factor of the sensitivity [4].
Acknowledgements
This work was supported by the Condensed Matter and Surface Science Program, Neuroscience Program and the Quantitative Biology Institute at Ohio University. AN acknowledges support from the RSF (Russia) grant 14-4100044. The authors thank A. L. Shilinikov, B. Lindner, D. F. Russell, and M. H. Rowe for valuable discussions.
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