On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings
We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system whe...
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Zusammenfassung: | We put forward the dynamical study of a novel higher-order small network of
Chialvo neurons arranged in a ring-star topology, with the neurons interacting
via linear diffusive couplings. This model is perceived to imitate the
nonlinear dynamical properties exhibited by a realistic nervous system where
the neurons transfer information through higher-order multi-body interactions.
We first analyze our model using the tools from nonlinear dynamics literature:
fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the
coexistence of chaotic attractors, and also an intriguing route to chaos
starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed
invariant curves, to ultimately chaos. We numerically observe the existence of
codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark
Sacker. We also qualitatively study the typical phase portraits of the system
and numerically quantify chaos and complexity using the 0-1 test and sample
entropy measure respectively. Finally, we study the collective behavior of the
neurons in terms of two synchronization measures: the cross-correlation
coefficient, and the Kuramoto order parameter. |
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DOI: | 10.48550/arxiv.2405.06000 |