The subtle changes occurring in complex dynamic systems are impacted by numerous highly interdependent components with nonlinear interactions, which may not be duly predicted only through the analyses of their separate individual parts. The recent technological advances have enabled the monitoring and managing of the systems on a timely basis even during the transient processes involved. Thus, the examination of rapidly evolving systems is observed at the levels of micro-scale, meso-scale and macro-scale in many relevant applications. Such a multidimensional framework can provide a robust means to understand and handle the inherent dynamics of complex systems. Numerous phenomena in nature display highly nonlinear dynamical characteristics in their own systems. For instance, while the atmosphere could be represented by a set of physical equations including energy balances, hydrology-related cycles and Navier–Stokes equations, and so forth, fractal indices characterize the generalization of the Euclidean or ordinary measurements, suggesting the representation of the relevant variables’ complexity by non-integer values.

Geometric trails can be employed for identifying and analyzing the complexity of observed phenomena which entail examination at different ranges from classical perspectives of fractal-based techniques to newer perspectives at temporal and spatial scales so that the features can be detected, identified and classified accurately. At this point, fractal geometry referring to the geometry of self-similarity where an object appears to show resemblance at different scales comes to the fore as an evident notion while one is observing features that occur naturally. The presence of chaos in the dynamics of transient phenomena reveals the extensive inherence of chaos at the essence of any deterministic climate model, which indicates that unpredictability is a globally widespread phenomenon through constructive interactions across the components of the related system. Mathematical modeling of changeable phenomena with fractal geometry and complex systems can offer a relatively holistic perspective for comprehending and predicting different environmental behaviors. The function of fractal geometry here is to provide the means for analyzing the self-similar and irregular patterns in natural phenomena, including dynamical systems, formation of cloud, temperature variability, and so on. Taken together, the applications of fractal geometry and mathematics combined with their rigor and computational techniques enable further understanding of fractals, complex dynamics, chaos, mathematical visualization, scale invariance, fractal geometry, among many other domains of natural sciences, science and engineering.

Based on these dynamical features, notions and applicability affordances, the aim of our special session is to explore the connections between fractal geometry, complex systems, data science, discrete mathematics, mathematical modeling, Artificial Intelligence (AI), machine learning, among others, by uncovering their implications in scientific research, systems theories and engineering practices.

The topics include but are not limited to:

• Self-similarity in biological systems and / or epidemiological dynamics
• Fractal antennas and signal processing
• Modeling chaotic patterns in nature and engineering
• Nanomaterials in species microorganisms
• Climate modeling, fractals, complexity and data science
• Emergence, feedback loops, and networked behavior
• Complex adaptive systems in ecological and economic modeling
• Systems thinking in engineering designs
• Discrete mathematics
• Machine learning in modeling complex behaviors
• Visualization of high-dimensional, fractal-like data
• Vibration analysis
• Role of AI in complex system optimization
• Identifying and modeling roles in collaborative networks
• Role mining in organizational and scientific workflows
• Applications in social network analysis and robotics
• Engineering mathematics
• Biomedical systems and role-based diagnostics