We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Dynamics and Jacobi stability of the controlled 3D Hindmarsh-Rose neuron model.
- Authors
Yang, Qigui; Lu, Xiaoting
- Abstract
This paper proposes the controlled 3D Hindmarsh-Rose neuron model with hidden chaos. We systematically study the internal characteristics of the kinetic generation mechanism of this model such as Lyapunov stability, codimension-one bifurcation, discharge patterns and energy consumption, Jacobi stability and two-parameter dynamics. Numerical simulations show that the model exhibits several types of complex phenomena, including periodic attractors, period-adding bifurcation into chaos, inverse period-doubling bifurcation into chaos and hidden chaos. Based on the Helmholtz theorem, Hamilton energy function is calculated. The energy consumption during the transition between different discharge patterns (including chaotic discharge and hidden discharge) is further estimated. From a geometric perspective, the Jacobi stability of the trajectories are investigated by using the KCC theory, including equilibria and periodic orbits. It is shown that some equilibria and two periodic orbits are Jacobi unstable in the sense of Lyapunov stable. More interestingly, in two-parameter region with Lyapunov stable but Jacobi unstable equilibrium, one not only observes that dynamical states alternate between periodic and chaotic dynamics, but also finds that the Hamilton energy corresponding to this region presents irregular oscillations. Moreover, dynamics of the deviation vector near equilibrium are depicted.
- Subjects
HELMHOLTZ, Hermann von, 1821-1894; LYAPUNOV stability; NEURONS; ENERGY function; ENERGY consumption; ORBITS (Astronomy)
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2024, Vol 29, Issue 5, p1
- ISSN
1531-3492
- Publication type
Article
- DOI
10.3934/dcdsb.2023175