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1.
1. B. C. Dickerson and H. Eichenbaum, “ The episodic memory system: Neurocircuitry and disorders,” Neuropsychopharmacology 35, 86104 (2010).
http://dx.doi.org/10.1038/npp.2009.126
2.
2. V. A. Diwadkar, P. A. Carpenter, and M. A. Just, “ Collaborative activity between parietal and dorso-lateral prefrontal cortex in dynamic spatial working memory revealed by fMRI,” Neuroimage 12, 8599 (2000).
http://dx.doi.org/10.1006/nimg.2000.0586
3.
3. K. Nashiro and M. Mather, “ The effect of emotional arousal on memory binding in normal aging and Alzheimer's disease,” Am. J. Psychol. 124, 301312 (2011).
http://dx.doi.org/10.5406/amerjpsyc.124.3.0301
4.
4. M. Rabinovich, A. Volkovskii, P. Lecanda, R. Huerta, H. Abarbanel, and G. Laurent, “ Dynamical encoding by networks of competing neuron groups: Winnerless competition,” Phys. Rev. Lett. 87, 068102 (2001).
http://dx.doi.org/10.1103/PhysRevLett.87.068102
5.
5. M. I. Rabinovich, R. Huerta, P. Varona, and V. S. Afraimovich, “ Transient cognitive dynamics, metastability, and decision making,” PLoS Comput. Biol. 4, e1000072 (2008).
http://dx.doi.org/10.1371/journal.pcbi.1000072
6.
6. M. I. Rabinovich, K. J. Friston, and P. Varona, Principles of Brain Dynamics: Global State Interactions ( MIT Press, 2012).
7.
7. C. Bick and M. I. Rabinovich, “ Dynamical origin of the effective storage capacity in the brain's working memory,” Phys. Rev. Lett. 103, 218101 (2009).
http://dx.doi.org/10.1103/PhysRevLett.103.218101
8.
8. K. Friston, C. Frith, and R. Frackowiak, “ Principal component analysis learning algorithms: A neurobiological analysis,” Proc. R. Soc. London, Ser. B 254, 4754 (1993).
http://dx.doi.org/10.1098/rspb.1993.0125
9.
9. J. Kelso, A. Fuchs, R. Lancaster, T. Holroyd, D. Cheyne, and H. Weinberg, “ Dynamic cortical activity in the human brain reveals motor equivalence,” Nature 392, 814818 (1998).
http://dx.doi.org/10.1038/33922
10.
10. A. McIntosh, F. Bookstein, J. V. Haxby, and C. Grady, “ Spatial pattern analysis of functional brain images using partial least squares,” Neuroimage 3, 143157 (1996).
http://dx.doi.org/10.1006/nimg.1996.0016
11.
11. A. J. Bell and T. J. Sejnowski, “ An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7, 11291159 (1995).
http://dx.doi.org/10.1162/neco.1995.7.6.1129
12.
12. S. Makeig, T. P. Jung, A. J. Bell, D. Ghahremani, and T. J. Sejnowski, “ Blind separation of auditory event-related brain responses into independent components,” Proc. Natl. Acad. Sci. 94, 1097910984 (1997).
http://dx.doi.org/10.1073/pnas.94.20.10979
13.
13. A. Banerjee, A. S. Pillai, and B. Horwitz, “ Using large-scale neural models to interpret connectivity measures of cortico-cortical dynamics at millisecond temporal resolution,” Front. Syst. Neurosci. 5, 102 (2011).
http://dx.doi.org/10.3389/fnsys.2011.00102
14.
14. M. I. Rabinovich, V. S. Afraimovich, and P. Varona, “ Heteroclinic binding,” Dyn. Syst. 25, 433442 (2010).
http://dx.doi.org/10.1080/14689367.2010.515396
15.
15. M. I. Rabinovich, A. N. Simmons, and P. Varona, “ Dynamical bridge between brain and mind,” Trends Cognit. Sci. 19, 453461 (2015).
http://dx.doi.org/10.1016/j.tics.2015.06.005
16.
16. V. Afraimovich and S. Hsu, Lectures on Chaotic Dynamical Systems ( American Mathematical Society Providence, 2003).
17.
17. A. Bystritsky, A. Nierenberg, J. Feusner, and M. Rabinovich, “ Computational non-linear dynamical psychiatry: A new methodological paradigm for diagnosis and course of illness,” J. Psychiatr. Res. 46, 428435 (2012).
http://dx.doi.org/10.1016/j.jpsychires.2011.10.013
18.
18. G. Schiepek, I. Tominschek, S. Heinzel, M. Aigner, M. Dold, A. Unger, G. Lenz, C. Windischberger, E. Moser, M. Plöderl et al., “ Discontinuous patterns of brain activation in the psychotherapy process of obsessive compulsive disorder: Converging results from repeated FMRI and daily self-reports,” PloS One 8, e71863 (2013).
http://dx.doi.org/10.1371/journal.pone.0071863
19.
19. A. M. Hayes, C. Yasinski, J. B. Barnes, and C. L. Bockting, “ Network destabilization and transition in depression: New methods for studying the dynamics of therapeutic change,” Clin. Psychol. Rev. (2015).
http://dx.doi.org/10.1016/j.cpr.2015.06.007
20.
20. R. A. Stevenson, M. Segers, S. Ferber, M. D. Barense, and M. T. Wallace, “ The impact of multisensory integration deficits on speech perception in children with autism spectrum disorders,” Front. Psychol. 5, 379 (2014).
http://dx.doi.org/10.3389/fpsyg.2014.00379
21.
21. M. T. Wallace and R. A. Stevenson, “ The construct of the multisensory temporal binding window and its dysregulation in developmental disabilities,” Neuropsychologia 64, 105123 (2014).
http://dx.doi.org/10.1016/j.neuropsychologia.2014.08.005
22.
22. A. R. Powers, A. R. Hillock, and M. T. Wallace, “ Perceptual training narrows the temporal window of multisensory binding,” J. Neurosci. 29, 1226512274 (2009).
http://dx.doi.org/10.1523/JNEUROSCI.3501-09.2009
23.
23. M. Quak, R. E. London, and D. Talsma, “ A multisensory perspective of working memory,” Front. Human Neurosci. 9, 197 (2015).
http://dx.doi.org/10.3389/fnhum.2015.00197
24.
24. D. Talsma, “ Predictive coding and multisensory integration: An attentional account of the multisensory mind,” Front. Integr. Neurosci. 9, 19 (2015).
http://dx.doi.org/10.3389/fnint.2015.00019
25.
25. R. M. May and W. J. Leonard, “ Nonlinear aspects of competition between three species,” SIAM J. Appl. Math. 29, 243253 (1975).
http://dx.doi.org/10.1137/0129022
26.
26. D. F. Toupo and S. H. Strogatz, “ Nonlinear dynamics of the rock-paper-scissors game with mutations,” Phys. Rev. E 91, 052907 (2015).
http://dx.doi.org/10.1103/PhysRevE.91.052907
27.
27. M. E. Gilpin, “ Limit cycles in competition communities,” Am. Nat. 109, 5160 (1975).
http://dx.doi.org/10.1086/282973
28.
28. J. Hofbauer and J.-H. So, “ Multiple limit cycles for three dimensional Lotka-Volterra equations,” Appl. Math. Lett. 7, 6570 (1994).
http://dx.doi.org/10.1016/0893-9659(94)90095-7
29.
29. M. Rabinovich, I. Tristan, and P. Varona, “ Neural dynamics of attentional cross-modality control,” PLoS ONE 8, e64406 (2013).
http://dx.doi.org/10.1371/journal.pone.0064406
30.
30. L. Glass and J. S. Pasternack, “ Prediction of limit cycles in mathematical models of biological oscillations,” Bull. Math. Biol. 40, 2744 (1978).
http://dx.doi.org/10.1007/BF02463128
31.
31. J. Vano, J. Wildenberg, M. Anderson, J. Noel, and J. Sprott, “ Chaos in low-dimensional Lotka-Volterra models of competition,” Nonlinearity 19, 2391 (2006).
http://dx.doi.org/10.1088/0951-7715/19/10/006
32.
32. V. Afraimovich, G. Moses, and T. Young, “ Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system,” Nonlinearity (submitted), arXiv:1509.04570 [math.DS]; available at http://arxiv.org/abs/1509.04570.
33.
33. M. I. Rabinovich, Y. Sokolov, and R. Kozma, “ Robust sequential working memory recall in heterogeneous cognitive networks,” Front. Syst. Neurosci. 8, 220 (2014).
http://dx.doi.org/10.3389/fnsys.2014.00220
34.
34. M. I. Rabinovich, P. Varona, A. I. Selverston, and H. D. Abarbanel, “ Dynamical principles in neuroscience,” Rev. Mod. Phys. 78, 1213 (2006).
http://dx.doi.org/10.1103/RevModPhys.78.1213
35.
35. O. Kolodny and S. Edelman, “ The problem of multimodal concurrent serial order in behavior,” Neuroscience & Biobehavioral Reviews 56, 252265 (2015).
http://dx.doi.org/10.1016/j.neubiorev.2015.07.009
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/content/aip/journal/chaos/25/10/10.1063/1.4932563
2015-10-13
2016-06-28

Abstract

Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories—episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree − 1, where is the number of modalities.

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