A novel conservative system with hidden flows evolved from the simplest memristive circuit

Prior research has extensively explored dissipative chaotic systems for various theoretical and practical purposes. These models often contain attractors that allow unauthorized parties to reconstruct sensitive information, creating significant security vulnerabilities. Conservative systems offer a distinct alternative by lacking these attractors, which inherently prevents such reconstruction attempts. Despite these advantages, the academic literature currently contains limited investigations into conservative dynamics. This gap motivated the development of new models that can better secure information in chaos-based applications. No prior work had resolved the challenge of creating a 3D conservative system without equilibria using memristive components. That uncertainty drove the need for a novel architecture that maintains complexity while ensuring security. This study addresses the lack of such systems by deriving a non-Hamiltonian model from a simple memristor circuit.

The aim of this study is to develop a novel 3D conservative system derived from the simplest memristor circuit. Researchers seek to address the information security vulnerabilities inherent in dissipative chaotic systems. These existing models are often susceptible to reconstruction attacks because they rely on attractors. The authors propose that a conservative architecture can effectively mitigate these risks by eliminating such attractors entirely. They focus on creating a non-Hamiltonian system that lacks equilibria to ensure unique dynamic properties. The investigation explores the phase volume conservatism through rigorous mathematical divergence analysis. Furthermore, the study evaluates the potential for high-quality pseudo-random number generation using statistical testing methods. Finally, the work intends to validate the theoretical findings through the design and implementation of a physical analog circuit.

The review approach involves deriving a non-Hamiltonian 3D model from a basic memristor-based architecture. Researchers calculate the divergence of the mathematical framework to verify phase volume conservatism. A Kolmogorov-type transformation is applied to evaluate the status of the Hamiltonian energy. The team investigates the existence of quasi-periodic 3D tori and heterogeneous coexisting trajectories triggered by varying initial values. To assess the utility of the model, the scientists perform Spectral Entropy analysis. They also conduct NIST testing to validate the randomness of the generated pseudo-random numbers. Finally, the group designs and implements an analog circuit to test the practical feasibility of the theoretical model. This comprehensive methodology ensures that both the mathematical properties and physical performance are rigorously examined.

The strongest finding is that the system exhibits complex quasi-periodic 3D tori with heterogeneous coexisting and different amplitude rescaling trajectories. The model successfully operates as a non-Hamiltonian 3D conservative system without any equilibria. Divergence calculations confirm the phase volume conservatism of the proposed mathematical structure. A Kolmogorov-type transformation reveals that the Hamiltonian energy is not conserved within the system. Spectral entropy analysis demonstrates that the model produces pseudo-random numbers with high levels of randomness. NIST test results further validate the statistical quality of these generated sequences. The researchers report that this is the first 3D conservative system to demonstrate such complex dynamics in a memristive framework. Physical implementation of the analog circuit confirms the feasibility of the design for practical applications.

The authors propose a novel 3D conservative system derived from a simple memristor circuit. This model successfully avoids the presence of equilibria, which distinguishes it from traditional dissipative chaotic architectures. The researchers demonstrate that the system exhibits complex quasi-periodic tori with heterogeneous coexisting trajectories. Their analysis confirms that the Hamiltonian energy remains non-conservative within this specific mathematical framework. Spectral entropy evaluations and NIST testing indicate that the system generates pseudo-random numbers with high levels of randomness. The authors highlight that this represents a unique 3D conservative system with unprecedented dynamic complexity. Physical implementation of an analog circuit confirms the feasibility of the proposed theoretical design. These findings suggest that the system provides a robust foundation for future chaos-based information security applications.