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Barba-Franco JJ, Gallegos A, Jaimes-Reátegui R, Muñoz-Maciel J, Pisarchik AN. Dynamics of coexisting rotating waves in unidirectional rings of bistable Duffing oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:073126. [PMID: 37433655 DOI: 10.1063/5.0141054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2023] [Accepted: 06/23/2023] [Indexed: 07/13/2023]
Abstract
We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies.
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Affiliation(s)
- J J Barba-Franco
- Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Colonia Paseos de la Monta na, 47460 Lagos de Moreno, Jalisco, Mexico
| | - A Gallegos
- Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Colonia Paseos de la Monta na, 47460 Lagos de Moreno, Jalisco, Mexico
| | - R Jaimes-Reátegui
- Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Colonia Paseos de la Monta na, 47460 Lagos de Moreno, Jalisco, Mexico
| | - J Muñoz-Maciel
- Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Colonia Paseos de la Monta na, 47460 Lagos de Moreno, Jalisco, Mexico
| | - A N Pisarchik
- Center for Biomedical Technology, Universidad Politécnica de Madrid, Campus de Montegancedo, Pozuelo de Alarcón, 28223 Madrid, Spain
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Makarov VA, Lobov SA, Shchanikov S, Mikhaylov A, Kazantsev VB. Toward Reflective Spiking Neural Networks Exploiting Memristive Devices. Front Comput Neurosci 2022; 16:859874. [PMID: 35782090 PMCID: PMC9243340 DOI: 10.3389/fncom.2022.859874] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 05/10/2022] [Indexed: 11/29/2022] Open
Abstract
The design of modern convolutional artificial neural networks (ANNs) composed of formal neurons copies the architecture of the visual cortex. Signals proceed through a hierarchy, where receptive fields become increasingly more complex and coding sparse. Nowadays, ANNs outperform humans in controlled pattern recognition tasks yet remain far behind in cognition. In part, it happens due to limited knowledge about the higher echelons of the brain hierarchy, where neurons actively generate predictions about what will happen next, i.e., the information processing jumps from reflex to reflection. In this study, we forecast that spiking neural networks (SNNs) can achieve the next qualitative leap. Reflective SNNs may take advantage of their intrinsic dynamics and mimic complex, not reflex-based, brain actions. They also enable a significant reduction in energy consumption. However, the training of SNNs is a challenging problem, strongly limiting their deployment. We then briefly overview new insights provided by the concept of a high-dimensional brain, which has been put forward to explain the potential power of single neurons in higher brain stations and deep SNN layers. Finally, we discuss the prospect of implementing neural networks in memristive systems. Such systems can densely pack on a chip 2D or 3D arrays of plastic synaptic contacts directly processing analog information. Thus, memristive devices are a good candidate for implementing in-memory and in-sensor computing. Then, memristive SNNs can diverge from the development of ANNs and build their niche, cognitive, or reflective computations.
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Affiliation(s)
- Valeri A. Makarov
- Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- *Correspondence: Valeri A. Makarov,
| | - Sergey A. Lobov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Sergey Shchanikov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Department of Information Technologies, Vladimir State University, Vladimir, Russia
| | - Alexey Mikhaylov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Viktor B. Kazantsev
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
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Propagating wave activity in a tangential cortical slice. Neuroreport 2021; 31:332-337. [PMID: 32058429 DOI: 10.1097/wnr.0000000000001408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
Propagating neural waves in the cerebral cortex influence the integration of incoming sensory information with ongoing cortical activity. However, the neural circuit elements that support these cortical waves remain to be fully defined. Here, a novel tangential slice preparation was developed that exhibited propagating wave activity across the dorsal cortical sheet, as assessed using autofluorescence imaging following focal electrical stimulation. Analysis of functional connectivity in the slice preparation with laser-scanning photostimulation via glutamate uncaging revealed a lack of short-latency, presumed monosynaptic, long-range connections (>300 μm) in the slice preparation. These results establish a novel slice preparation for assessing cortical dynamics and support the proposition that interactions among local cortical elements are sufficient to enable widespread propagating wave activity.
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