1
|
A hierarchical model of perceptual multistability involving interocular grouping. J Comput Neurosci 2020; 48:177-192. [PMID: 32338341 DOI: 10.1007/s10827-020-00743-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Revised: 02/04/2020] [Accepted: 02/11/2020] [Indexed: 10/24/2022]
Abstract
Ambiguous visual images can generate dynamic and stochastic switches in perceptual interpretation known as perceptual rivalry. Such dynamics have primarily been studied in the context of rivalry between two percepts, but there is growing interest in the neural mechanisms that drive rivalry between more than two percepts. In recent experiments, we showed that split images presented to each eye lead to subjects perceiving four stochastically alternating percepts (Jacot-Guillarmod et al. Vision research, 133, 37-46, 2017): two single eye images and two interocularly grouped images. Here we propose a hierarchical neural network model that exhibits dynamics consistent with our experimental observations. The model consists of two levels, with the first representing monocular activity, and the second representing activity in higher visual areas. The model produces stochastically switching solutions, whose dependence on task parameters is consistent with four generalized Levelt Propositions, and with experiments. Moreover, dynamics restricted to invariant subspaces of the model demonstrate simpler forms of bistable rivalry. Thus, our hierarchical model generalizes past, validated models of binocular rivalry. This neuromechanistic model also allows us to probe the roles of interactions between populations at the network level. Generalized Levelt's Propositions hold as long as feedback from the higher to lower visual areas is weak, and the adaptation and mutual inhibition at the higher level is not too strong. Our results suggest constraints on the architecture of the visual system and show that complex visual stimuli can be used in perceptual rivalry experiments to develop more detailed mechanistic models of perceptual processing.
Collapse
|
2
|
Pérez-Cervera A, Ashwin P, Huguet G, M Seara T, Rankin J. The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2019; 9:7. [PMID: 31385150 PMCID: PMC6682846 DOI: 10.1186/s13408-019-0075-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2019] [Accepted: 06/19/2019] [Indexed: 06/01/2023]
Abstract
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter ϵ uncouples the system at [Formula: see text]. Using a normal form for [Formula: see text] identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in the existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down.
Collapse
Affiliation(s)
- Alberto Pérez-Cervera
- Departament de Matemàtiques - BGSMATH, Universitat Politècnica de Catalunya, Barcelona, Spain.
| | - Peter Ashwin
- Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
- EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, UK
| | - Gemma Huguet
- Departament de Matemàtiques - BGSMATH, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Tere M Seara
- Departament de Matemàtiques - BGSMATH, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - James Rankin
- Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
- EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, UK
| |
Collapse
|
3
|
Akcay Z, Huang X, Nadim F, Bose A. Phase-locking and bistability in neuronal networks with synaptic depression. PHYSICA D. NONLINEAR PHENOMENA 2018; 364:8-21. [PMID: 31462839 PMCID: PMC6713463 DOI: 10.1016/j.physd.2017.09.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris-Lecar neuron models.
Collapse
Affiliation(s)
- Zeynep Akcay
- Department of Mathematics and Computer Science, Queensborough Community College, Bayside, NY 11364, USA
| | - Xinxian Huang
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA
| | - Farzan Nadim
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA
- Federated Department of Biological Sciences, New Jersey Institute of Technology and Rutgers University, Newark, NJ 07102, USA
| | - Amitabha Bose
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA
| |
Collapse
|
4
|
Romeo A, Supèr H. 'Two vs one' rivalry by the Loxley-Robinson model. BIOLOGICAL CYBERNETICS 2017; 111:405-420. [PMID: 28929217 DOI: 10.1007/s00422-017-0734-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 09/06/2017] [Indexed: 06/07/2023]
Abstract
We apply the competitive model of Loxley and Robinson (Phys Rev Lett 102:258701, 2009. doi: 10.1103/PhysRevLett.102.258701 ) to the study of a special case of visual rivalry. Three-peaked inputs with maxima at symmetrical locations are introduced, and the role of three-bump configurations is then considered. The model yields conditions for what can be interpreted as a bistable percept analogous to the one-dimensional version of a competition between the central and flanking parts of an image.
Collapse
Affiliation(s)
- August Romeo
- Department of Cognition, Development and Educational Psychology, Faculty of Psychology, University of Barcelona (UB), Barcelona, Spain
| | - Hans Supèr
- Department of Cognition, Development and Educational Psychology, Faculty of Psychology, University of Barcelona (UB), Barcelona, Spain.
- Institut de Neurociències, University of Barcelona (UB), Barcelona, Spain.
- Catalan Institution for Research and Advanced Studies (ICREA), Barcelona, Spain.
| |
Collapse
|
5
|
Sensory feedback in a bump attractor model of path integration. J Comput Neurosci 2016; 40:137-55. [PMID: 26754972 DOI: 10.1007/s10827-015-0588-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Revised: 12/14/2015] [Accepted: 12/22/2015] [Indexed: 10/24/2022]
Abstract
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.
Collapse
|
6
|
Abstract
Attractor models are simplified models used to describe the dynamics of firing rate profiles of a pool of neurons. The firing rate profile, or the neuronal activity, is thought to carry information. Continuous attractor neural networks (CANNs) describe the neural processing of continuous information such as object position, object orientation, and direction of object motion. Recently it was found that in one-dimensional CANNs, short-term synaptic depression can destabilize bump-shaped neuronal attractor activity profiles. In this article, we study two-dimensional CANNs with short-term synaptic depression and spike frequency adaptation. We found that the dynamics of CANNs with short-term synaptic depression and CANNs with spike frequency adaptation are qualitatively similar. We also found that in both kinds of CANNs, the perturbative approach can be used to predict phase diagrams, dynamical variables, and speed of spontaneous motion.
Collapse
Affiliation(s)
- C C Alan Fung
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | | |
Collapse
|
7
|
Rankin J, Meso AI, Masson GS, Faugeras O, Kornprobst P. Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration. J Comput Neurosci 2014; 36:193-213. [PMID: 24014258 PMCID: PMC3950608 DOI: 10.1007/s10827-013-0465-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2013] [Revised: 05/19/2013] [Accepted: 05/20/2013] [Indexed: 11/17/2022]
Abstract
Perceptual multistability is a phenomenon in which alternate interpretations of a fixed stimulus are perceived intermittently. Although correlates between activity in specific cortical areas and perception have been found, the complex patterns of activity and the underlying mechanisms that gate multistable perception are little understood. Here, we present a neural field competition model in which competing states are represented in a continuous feature space. Bifurcation analysis is used to describe the different types of complex spatio-temporal dynamics produced by the model in terms of several parameters and for different inputs. The dynamics of the model was then compared to human perception investigated psychophysically during long presentations of an ambiguous, multistable motion pattern known as the barberpole illusion. In order to do this, the model is operated in a parameter range where known physiological response properties are reproduced whilst also working close to bifurcation. The model accounts for characteristic behaviour from the psychophysical experiments in terms of the type of switching observed and changes in the rate of switching with respect to contrast. In this way, the modelling study sheds light on the underlying mechanisms that drive perceptual switching in different contrast regimes. The general approach presented is applicable to a broad range of perceptual competition problems in which spatial interactions play a role.
Collapse
Affiliation(s)
- J Rankin
- Neuromathcomp Team, Inria Sophia Antipolis, 2004 Route des Lucioles-BP 93, Alpes-Maritimes, 06902, France,
| | | | | | | | | |
Collapse
|
8
|
Fung CCA, Wang H, Lam K, Wong KYM, Wu S. Resolution enhancement in neural networks with dynamical synapses. Front Comput Neurosci 2013; 7:73. [PMID: 23781197 PMCID: PMC3677988 DOI: 10.3389/fncom.2013.00073] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2013] [Accepted: 05/15/2013] [Indexed: 11/29/2022] Open
Abstract
Conventionally, information is represented by spike rates in the neural system. Here, we consider the ability of temporally modulated activities in neuronal networks to carry information extra to spike rates. These temporal modulations, commonly known as population spikes, are due to the presence of synaptic depression in a neuronal network model. We discuss its relevance to an experiment on transparent motions in macaque monkeys by Treue et al. in 2000. They found that if the moving directions of objects are too close, the firing rate profile will be very similar to that with one direction. As the difference in the moving directions of objects is large enough, the neuronal system would respond in such a way that the network enhances the resolution in the moving directions of the objects. In this paper, we propose that this behavior can be reproduced by neural networks with dynamical synapses when there are multiple external inputs. We will demonstrate how resolution enhancement can be achieved, and discuss the conditions under which temporally modulated activities are able to enhance information processing performances in general.
Collapse
Affiliation(s)
- C C Alan Fung
- Department of Physics, The Hong Kong University of Science and Technology Hong Kong, China
| | | | | | | | | |
Collapse
|