BLOW-UP CRITERION IN THE LORENZ SYSTEM

This paper explores the application of blow-up criterion to Lorenz system establish possibility a finite-time outburst when quadratic term is present. The system, set differential equations that models atmospheric convection, known for its chaotic behavior and has been subject extensive research because sensitivity initial conditions. By analyzing using criterion, conditions under which can lead solution becomes infinite in finite time are investigated. notion great importance theory partial dynamical systems. In addition, study focuses on various ways nonlinear terms avoid blowup maintain bounded stable solution. sheds light complex relationship between Lorentz nonlinearities occurrence bursting phenomena. Understanding these mechanisms crucial predicting controlling systems with terms, especially context convection other conclusion, analysis opens new perspectives findings presented here may have applications climate prediction understanding dynamics areas science engineering. Keywords: Blow-Up Criterion, System, Attractor, Maximal Interval DOI： https://doi.org/10.35741/issn.0258-2724.58.4.64