Co- Chairs:

Prof. Mohammed Salah Abdelouahab, Abdelhafid Boussouf University Center of Mila, Department of Mathematics, Mila, Algeria; e-mail: m.abdelouahab@centre-univ-mila.dz

Prof. Davide Radi,  Catholic University of Sacred Heart, Financial and Actuarial Sciences, Department of Mathematics for Economic, Milan, Italy; e-mail: davide.radi@unicatt.it

Nonlinear maps signify mathematical functions describing the systems’ evolution, in which the relationship between the variables is not linear. Owing to these aspects, nonlinear maps are frequently employed to model complex, dynamic systems manifesting behaviors like bifurcation, oscillations and chaos. Nonlinear maps are employed as they are computationally less burdensome by retaining the chaotic systems’ fundamental features, shedding light on the chaotic attractors’ dynamics and structure as well as serving as a benchmark to test algorithms in cryptography and chaos theory. Overall, recent progresses in chaotic systems, bifurcation theory, nonlinear circuits and wavelet-based techniques have revealed new potentials in secure communication, financial analysis and epidemiology. Advances in chaos-based encryption, machine learning models and predictive analytics have further expanded their impact across multiple fields. A key application, for example, is the use of chaotic circuits and nonlinear maps for image encryption and secure data transmission, which attempt to reduce unpredictability for enhancing multimedia security. At this juncture, wavelet-based techniques have been widely applied in chaotic signal processing, noise reduction as well as image enhancement.

These significant features are critical in settings where unpredictability and complicatedness are conspicuous. Coupled nonlinear maps, on the other hand, are acknowledged as mathematical models with multiple nonlinear systems or maps being interconnected, evolving over discrete time steps and manifesting chaotic behaviors very often. The benefits of coupled nonlinear maps are evident in stability analysis and scalability in large-scale systems that have numerous interacting components.

Chaos-driven learning algorithms and neural networks for modeling chaotic time series have gained more prominence, through applications in finance, biomedical imaging and system modeling. In economic research, for instance, chaotic models help analyze nonlinear market dynamics, digital oligopolies and financial fluctuations, while wavelet-based forecasting techniques can be employed to improve financial trend predictions. Chaos computing, as a new paradigm in relation with unconventional computing by being a candidate for replacing conventional computing technologies, makes use of extreme non–linearity of chaotic systems whose complex dynamics can carry out computations. Computation of chaotic solutions entails solving mathematical models that exhibit chaotic behaviors, which can often be derived from nonlinear differential equations, difference equations, iterative maps, and so forth. In biomedical and epidemiological research, fractional-order nonlinear models play a significant role in medical imaging and epidemic forecasting. Integrating chaos theory with deep learning enhances disease spread predictions besides reinforcing public health policies and interventions. Nonlinear maps and chaos computing are at use in many systems such as neural and other networks, ecosystems, dynamics of celestial bodies, optimizing processes, control systems for chaotic environments, evolutionary algorithms among others. These processes display their benefits through predictive power, forecasting capabilities along with realization of innovations in various technologies and industries.

Based on these theoretical foundations and applicability aspects, the aim of our special session is to explore advances, highlight novel methodologies and practical implementations regarding the applicability of nonlinear maps, chaos computing as well as progresses in chaos theory and wavelet applications span across various fields and domains, including applied mathematics, physics, cryptography, computational sciences, information science, biology, public health, environmental sciences, network science, engineering, cryptography, to name some to be able to foster interdisciplinary collaboration and advance the field further.

The key topics include but are not limited to: