Global Dynamics of Nonautonomous Hindmarsh-Rose Equations
Chi Phan, Yuncheng You
TL;DR
This paper investigates the global behavior of nonautonomous Hindmarsh-Rose equations in neurodynamics, establishing the existence of pullback and exponential attractors through advanced mathematical analysis.
Contribution
It proves the existence of pullback and exponential attractors for nonautonomous Hindmarsh-Rose equations, advancing understanding of their long-term dynamics.
Findings
Existence of pullback attractor established.
Existence of pullback exponential attractor proved.
Solutions exhibit long-term smoothing and dissipative properties.
Abstract
Global dynamics of nonautonomous diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback dissipative property and the pullback asymptotical compactness. Then the existence of pullback exponential attractor is also established by proving the smoothing Lipschitz continuity in a long run of the solution process.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsstochastic dynamics and bifurcation · Advanced Thermodynamics and Statistical Mechanics · Nonlinear Dynamics and Pattern Formation