J. Nonlinear Sci. Appl., 14 (2021), 15–28 ISSN: 2008-1898 Journal Homepage: www.isr-publications.com/jnsa Nonlinear dynamics and synchronization of computational cognitive model in educational science Ekemini T. Akpan a,* , Enobong E. Joshua b , Ignatius E. Uduk c a Department of Science Education, Mathematics Unit, Faculty of Education, University of Uyo, Uyo. b Department of Mathematics, Faculty of Science, University of Uyo, Uyo. c Department of Human Kinetics, Faculty of Education, University of Uyo, Uyo. Abstract A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostkian constructs to explain, and predict cognitive processes during collaborative learning. Learning is re-conceptualized as continuous perturbations of cog- nitive state which unfolds stable cognitive trajectories near Piagetian equilibrium. The model explicates topologically equivalent cognitive patterns, attributed to multi-modal representation of sensory information presented to the learners. Synchronization of the cognitive model is obtained via active control functions which predicts convergence of cognitive states. The synchronized cognitive model is stabilized using Lyapunov matrix equation. These qualitative behaviors emerged due to learner-to-learner and instructor-to-learner scaffolding driven by cognitive executive functions. The dynamical behaviors of the cognitive model are simulated using control parameters with estimated datasets showing viable cognitive trajectories. Keywords: Cognitive model, equilibrium, learning, stability, synchronization, Lyapunov matrix equation. 2020 MSC: 37C75, 91E10, 97C30, 97M10. c 2021 All rights reserved. 1. Introduction Recent studies in Mathematical Psychology shows that Neo-Vygostkian and Neo-Piagetian constructs are requisite verbalized theories that link science education research and complex nonlinear dynamical systems [28, 31, 34]. Vygotskian constructs explain the theoretical and conceptual framework of collab- orative learning. Collaborative learning by nature, creates opportunities for learners to develop their cognition; thinking, reasoning, problem solving, and learning by active communication with more capa- ble peers (instructors) [15]. Also, Piagetian cognitive processes which focused on learners’ construction of their knowledge is intertwined with nonlinear dynamic behaviors; learners’ cognitive evolution over nested time scale [19, 29]. Transient cognitive dynamics and cusp catastrophe are robust qualitative behav- iors in Piagetian stage-wise cognitive development [21]. In [23], Piagetian core constructs; assimilation and accommodation processes are being modeled as independent control parameters that determine abrupt * Corresponding author Email addresses: ekeminitakpan@uniuyo.edu.ng (Ekemini T. Akpan), enobongjoshua@uniuyo.edu.ng (Enobong E. Joshua), ignatiusuduk@uniuyo.edu.ng (Ignatius E. Uduk) doi: 10.22436/jnsa.014.01.03 Received: 2020-02-19 Revised: 2020-04-30 Accepted: 2020-05-11