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The book examines various practical systems, including models of target detection in cells through the analysis of bio-nanomachine, attractant, and repellent concentrations. It addresses the quasistatic evolution of anelastic structures, explores the generation of triangular patterns through anisotropic diffusion, and discusses the stabilization of time-delay distributed bilinear systems in spatial domains. The book is designed for theorists, applied mathematicians, and engineers across diverse scientific disciplines, serving as a valuable resource for anyone interested in bifurcation theory’s wide-ranging applications. This volume is a collection of chapters that describe the theory and application of nonlinear dynamics to a wide variety of problems in physics and engineering. Each chapter is self-contained and includes an introduction, main contributions, and details of up-to-date theoretical, computational, and experimental results. Topics also include optimal control challenges in bilinear systems with unbounded and bounded control sets, forward bifurcation in hepatitis B virus infection models, and the bifurcation of hematological stem cells with feedback control in a biological context. Introduction to Tangent Vectors, Flows and Bifurcations Regional Weak and Strong Stabilization of Time Delay Infinite Dimensional Bilinear Systems On the Optimal Control Problem for Bilinear Systems with Bounded and Unbounded Controls Forward Bifurcation and Stability Analysis Stability Arguments in Molecular Communication Networks Stability and Bifurcation in Nonlinear Mechanics Bifurcation and Periodic Triangular Pattern Formation in Reaction-Diffusion with Anisotropic Diffusion Dynamics of a Neutrophil Model with State Feedback Control of Time Delay