English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We present a second-order extension of the first-order Lohe hermitiansphere(LHS) model and study its emergent asymptotic dynamics. Our proposedmodel incorporates an inertial effect as a second-order extension. The inertiaterm can generate an oscillatory behavior of particle trajectory in a smalltime interval(initial layer) which causes a technical difficulty for theapplication of monotonicity-based arguments. For emergent estimates, we employtwo-point correlation function which is defined as an inner product betweenpositions of particles. For a homogeneous ensemble with the same frequencymatrix, we provide two sufficient frameworks in terms of system parameters andinitial data to show that two-point correlation functions tend to the unitywhich is exactly the same as the complete aggregation. In contrast, for aheterogeneous ensemble with distinct frequency matrices, we provide asufficient framework in terms of system parameters and initial data, whichmakes two-point correlation functions close to unity by increasing theprincipal coupling strength.

Collective behaviors of the Lohe hermitian sphere model with inertia