TABU LEARNING NEURON MODEL: REVEALING ASYMMETRIC AND TRANSIENT PHENOMENA UNDER IMPERFECT SYMMETRY
Abstract
It is widely accepted that symmetries are rarely, if ever, exact in any biological system. Minimum imperfections and external perturbations are inevitable, meaning some degree of symmetry breaking must always be assumed present. However, within the field of computational neuroscience, only a limited number of studies have focused on the intrinsic dynamics of neural network models under conditions of imperfect symmetry. This paper directly addresses this gap by exploring the profound effects of deliberate symmetry breaking on the dynamics of the Tabu learning neuron (TLN) model. By introducing and varying a small symmetry perturbation parameter, we precisely control the model's symmetry and disclose a rich repertoire of previously unreported asymmetric dynamic behaviors. These include complex regimes of asymmetric multistability, where multiple distinct stable states coexist, and asymmetric chaotic bursting oscillations. Furthermore, we reveal the presence of several metastable or transient phenomena, such as transient asymmetric bursting oscillations and transient chaos, where the system exhibits complex behavior before eventually settling into a simpler attractor. These intricate dynamic features are systematically illustrated and verified by utilizing a suite of nonlinear investigation tools. Our methodology encompasses the analysis of time series, bifurcation diagrams, and one- and two-dimensional plots of the leading Lyapunov exponent, complemented by detailed plots of state space trajectories. The plethora of novel behaviors uncovered in this study, stemming directly from controlled symmetry imperfection, represents a significant contribution to the fields of nonlinear dynamics and neuromorphic modelling, highlighting the critical role of asymmetry in generating computational complexity.
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