This study develops a mathematical model of embodied cognition integrated with personalized learning within an interactive Virtual Reality (VR) environment, employing nonlinear systems theory to optimize educational outcomes. The study mathematically formulates the interactions between learners’ cognitive states, bodily actions, and environmental inputs by applying state-space models and multi-modal data analysis. The framework incorporates real-time affective feedback and dynamic adjustment mechanisms, improving mental performance and reducing cognitive load. A randomized controlled trial validates the model, demonstrating significant enhancements in learning satisfaction and knowledge retention. This research provides a novel quantitative basis for integrating nonlinear mathematical methods into the design and optimization of personalized learning systems in VR.

This paper sums up four security factors after analyzing co-residency threats caused by the special multitenant environment in the cloud. To secure the factors, a multiway dynamic trust chain transfer model was proposed on the basis of a measurement interactive virtual machine and current behavior to protect the integrity of the system. A trust chain construction module is designed in a virtual machine monitor. Through dynamic monitoring, it achieves the purpose of transferring integrity between virtual machine. A cloud system with a trust authentication function is implemented on the basis of the model, and its practicability is shown.

Virtual and augmented reality technology is increasingly used in the field of cultural creation, and intangible cultural heritage has become an important element in the field of cultural creation. Taking the intangible cultural heritage Suona art as an example, based on the analysis of Suona art background, development and communication status, this paper puts forward the design idea of the Suona virtual scene system. Using virtual display development engine Unreal Engine 4 and data import plug-in Datasmith, combined with LBS (location-based service) technology, the design and construction of the Suona art virtual scene are realized. The system analyzes the artistic characteristics of Suona's famous song " Birds paying homage to the Phoenix" and integrates it into the crescent spring scenic spot, which improves the immersion, interactivity and imagination of the scene experience. At the same time, the interactive system provides new ideas and effective practical solutions for the spread of Suona's intangible cultural heritage culture.