{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T06:02:45Z","timestamp":1760853765945},"reference-count":46,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p> In our previous studies, we showed that the both realistic and analytical computational models of neural dynamics can display multiple sustained states (attractors) for the same values of model parameters. Some of these states can represent normal activity while other, of oscillatory nature, may represent epileptic types of activity. We also showed that a simplified, analytical model can mimic this type of behavior and can be used instead of the realistic model for large scale simulations. The primary objective of the present work is to further explore the phenomenon of multiple stable states, co-existing in the same operational model, or phase space, in systems consisting of large number of interconnected basic units. As a second goal, we aim to specify the optimal method for state control of the system based on inducing state transitions using appropriate external stimulus. We use here interconnected model units that represent the behavior of neuronal populations as an effective dynamic system. The model unit is an analytical model (S. Kalitzin et al., Epilepsy Behav.\u00a022 (2011) S102\u2013S109) and does not correspond directly to realistic neuronal processes (excitatory\u2013inhibitory synaptic interactions, action potential generation). For certain parameter choices however it displays bistable dynamics imitating the behavior of realistic neural mass models. To analyze the collective behavior of the system we applied phase synchronization analysis (PSA), principal component analysis (PCA) and stability analysis using Lyapunov exponent (LE) estimation. We obtained a large variety of stable states with different dynamic characteristics, oscillatory modes and phase relations between the units. These states can be initiated by appropriate initial conditions; transitions between them can be induced stochastically by fluctuating variables (noise) or by specific inputs. We propose a method for optimal reactive control, allowing forced transitions from one state (attractor) into another. <\/jats:p>","DOI":"10.1142\/s0129065714500208","type":"journal-article","created":{"date-parts":[[2014,5,2]],"date-time":"2014-05-02T01:53:16Z","timestamp":1398995596000},"page":"1450020","source":"Crossref","is-referenced-by-count":34,"title":["MULTIPLE OSCILLATORY STATES IN MODELS OF COLLECTIVE NEURONAL DYNAMICS"],"prefix":"10.1142","volume":"24","author":[{"given":"STILIYAN","family":"KALITZIN","sequence":"first","affiliation":[{"name":"Foundation Epilepsy Institute in The Netherlands (SEIN), Achterweg 5, Heemstede, The Netherlands"}]},{"given":"MARCUS","family":"KOPPERT","sequence":"additional","affiliation":[{"name":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon EX4 4QF, UK"}]},{"given":"GEORGE","family":"PETKOV","sequence":"additional","affiliation":[{"name":"Foundation Epilepsy Institute in The Netherlands (SEIN), Achterweg 5, Heemstede, The Netherlands"},{"name":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon EX4 4QF, UK"}]},{"given":"FERNANDO LOPES","family":"DA SILVA","sequence":"additional","affiliation":[{"name":"Swammerdam Institute for Life Sciences, Center of Neuroscience, University of Amsterdam, Amsterdam, The Netherlands"},{"name":"Department of Bioengineering, Instituto Superior T\u00e9cnico, Lisbon Technical University, Lisbon, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2014,7,31]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.yebeh.2011.08.017"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/TNSRE.2005.847387"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00270757"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroscience.2004.03.014"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2005.869800"},{"key":"rf6","first-page":"288","volume":"22","author":"Suffczynski P.","year":"2005","journal-title":"J. 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