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Delay-Induced Complexity and Chaotic Dynamics in a Network Model of Information Spreading
Vasyl Martsenyuk1, Tomasz Gancarczyk1
1Department of Computer Science and Automatics, University of Bielsko-Biala, Willowa 2, 43-309 Bielsko-Biała, Poland.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
Time delays in network interactions significantly increase complexity and unpredictability in information spreading. This study models delayed interactions to reveal how they drive systems from stable states to chaotic dynamics.
Area of Science:
- Complex Systems
- Network Science
- Nonlinear Dynamics
Background:
- Information spreading in networks is crucial for understanding social dynamics.
- Real-world interactions often involve delays, impacting system behavior.
- Existing models may not fully capture the effects of these delays.
Purpose of the Study:
- Investigate the dynamical behavior of information spreading in a network with time delays.
- Analyze how time delay and interaction strength influence system complexity and stability.
- Develop a discrete-time network model incorporating delayed interactions.
Main Methods:
- Formulated a discrete-time network model using delay difference equations.
- Employed analytical techniques to determine steady states and their stability conditions.
- Utilized bifurcation analysis and Lyapunov exponent calculations for numerical simulations.
Main Results:
- Identified critical thresholds for qualitative transitions in system dynamics.
- Demonstrated a progression from stable equilibria to oscillatory and chaotic behaviors.
- Showcased the significant role of time delay in enhancing nonlinear complexity.
Conclusions:
- Time delays are fundamental in promoting unpredictable dynamics in networked systems.
- Findings enhance understanding of information propagation processes.
- Insights can inform the design and control of spreading phenomena in various networks.
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