Modeling of nonlinear dynamical systems based on deterministic learning and structural stability

Chen, Danfeng; Wang, Cong

doi:10.1109/chicc.2015.7259934

Cited by 2 publications

(1 citation statement)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the PE property, locally accurate NN identification of the unknown system topology can be achieved by using localized RBF networks even for a Lyapunov unstable system (Yuan and Wang 2011 ). The identified system topologies and dynamics were further applied to the dynamical modeling of nonlinear systems (Chen et al 2016a ), the bifurcation prediction of power systems (Chen and Wang 2016b ), and the heart valve disorder detection from PCG signals (Zeng et al 2021 ), and so on.…”

Section: Introductionmentioning

confidence: 99%

Topology identification and dynamical pattern recognition for Hindmarsh–Rose neuron model via deterministic learning

Chen

Zeng

et al. 2022

Cogn Neurodyn

View full text Add to dashboard Cite

Studies have shown that Parkinson’s, epilepsy and other brain deficits are closely related to the ability of neurons to synchronize with their neighbors. Therefore, the neurobiological mechanism and synchronization behavior of neurons has attracted much attention in recent years. In this contribution, it is numerically investigated the complex nonlinear behaviour of the Hindmarsh–Rose neuron system through the time responses, system bifurcation diagram and Lyapunov exponent under different system parameters. The system presents different and complex dynamic behaviors with the variation of parameter. Then, the identification of the nonlinear dynamics and topologies of the Hindmarsh–Rose neural networks under unknown dynamical environment is discussed. By using the deterministic learning algorithm, the unknown dynamics and topologies of the Hindmarsh–Rose system are locally accurately identified. Additionally, the identified system dynamics can be stored and represented in the form of constant neural networks due to the convergence of system parameters. Finally, based on the time-invariant representation of system dynamics, a fast dynamical pattern recognition method via system synchronization is constructed. The achievements of this work will provide more incentives and possibilities for biological experiments and medical treatment as well as other related clinical researches, such as the quantifying and explaining of neurobiological mechanism, early diagnosis, classification and control (treatment) of neurologic diseases, such as Parkinson’s and epilepsy. Simulations are included to verify the effectiveness of the proposed method.

show abstract