Chaos, whose principal feature is evidently random-like behavior, is bounded steady-state behavior that is not an equilibrium point, not periodic and not quasi-periodic. Extreme sensitivity of the system dynamics to its initial conditions with two significantly different asymptotic states of the system trajectory is another feature to be noted.  Chaotic systems, characterized by sensitivity to initial conditions alongside their inherent complexity, manifest their pertinence in theoretical research and practical applications. Manifesting seemingly random yet deterministic behaviors, these systems can be illustrated by various chaotic maps which allow for the modeling of different phenomena like chemical reactions, cryptographic algorithms, population dynamics, and so on. While chaotic oscillators are employed for secure communication systems, chaos-based optimizations can address complex problems in the areas of signal processing, cryptography, machine learning, artificial intelligence (AI), deep learning, to cite some.

Nonlinear dynamics and chaos theory have emerged as robust frameworks to understand complex patterns and behaviors across a broad spectrum of physical systems. Bifurcation is used to describe significant qualitative changes arising in the trajectories of a generally nonlinear dynamical system as the key system parameters are varied. Correspondingly, bifurcation theory, another layer added to the study of chaos, is oriented towards exploring how minor changes in the system parameters may cause major shifts in behavior, doing the transition from period to chaotic states. Nonlinear systems, being prevalent in natural and engineered environments, are systems that have behaviors governed by nonlinear relationship between the variables Multiple equilibria, sensitivity to initial conditions like in chaotic systems and bifurcations are among the fundamental characteristics of nonlinear systems. Bifurcation analysis is acknowledged to be a critical tool considering these systems and their mentioned characteristics. Signifying transitions between stable, periodic and chaotic states, bifurcation analysis can shed light on the evolution of chaos. Other concepts of synchronization and multistability can further supplement the understanding of chaotic systems. Stability involves the coordination of dynamics between coupled chaotic systems and has applications, whereas multistability denotes the coexistence of multiple stable states within a system, bringing about diverse and complex responses to small perturbations. As they have broad applicability areas, their analyses and applications can serve in different domains spanning from control theory to ecological and biological modeling, through computer science, applied mathematics, engineering, biology, biophysics, medicine, genetics, epidemiology, neuroscience, secure communication and engineering, to name some.

The aim of our special session is to explore and discuss the most recent advancements, technologies and applications concerning chaos, symmetry, synchronization and multistability, bifurcations, fractals, fractional, chaos-based technologies, AI and deep learning techniques among others by integrating and including diverse viewpoints on nonlinear dynamics, control systems, chaotic systems, other relevant systems and real-world settings. Consequently, we hope to promote fruitful discussions based on interdisciplinary theoretical frameworks with viable applications.

The topics include but are not limited to: