Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay by Qingyi Cui, Changjin Xu, Wei Ou, Yicheng Pang, Zixin Liu, Peiluan Li, Lingyun Yao

“…Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. …”
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Assessing the dynamics of bifurcation transformations in the economy by Vasilyeva Tetyana, Kuzmenko Olha, Bozhenko Victoria, Kolotilina Olena

“…Therefore, the study aims to quantitatively assess the level of transformations in the social, economic and political development of some European countries (Ukraine, France, Italy) using bifurcation theory for the period of 2000-2017. The proposed scientific and methodological approach to assessing the level of transformations in the social, economic and political development of a particular country involves the step-wise implementation: 1) the formation of an information base for the study, which involves collecting and testing statistical data for anomaly detection using the Irwin method, and selecting relevant indicators affecting the social, political and economic situation based on the principal component analysis; 2) the normalization of indicators of the political, economic and social situation using the Harrington’s approach; 3) the formation of integral indicators of the social, political and economic situation in the country based on the convolution of normalized indicators; 4) the determination of the dynamic properties of the social, political and economic situation in the country by constructing differential equations, which allows determining the existence of a bifurcation type (saddle, focus, node). …”
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Eddy viscosity modeling around curved boundaries through bifurcation approach and theory of rotating turbulence by Toh, Yi Han, Ng, Bing Feng

“…A novel approach to curvature effects based on the bifurcation theory and rotation turbulence energy spectrum is implemented to improve the sensitivity of the k−ϵ two-equation turbulence model (Jones-Launder form) to curved surfaces. …”
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Schistosomiasis model with treatment, habitat modification and biological control by Wahyudin Nur, Trisilowati, Agus Suryanto, Wuryansari Muharini Kusumawinahyu

“…Linearization combined with the Routh-Hurwitz criterion is used to prove the local stability condition of disease-free equilibrium points. Bifurcation theory is applied to investigate the local stability condition of the endemic equilibrium points. …”
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Mechanisms of left-right coordination in mammalian locomotor pattern generation circuits: a mathematical modeling view. by Yaroslav I Molkov, Bartholomew J Bacak, Adolfo E Talpalar, Ilya A Rybak

“…The model demonstrated a typical left-right alternating pattern under control conditions, switching to a hopping activity at any frequency after removing both V0 connections, a synchronized pattern at low frequencies with alternation at high frequencies after removing only V0D connections, and an alternating pattern at low frequencies with hopping at high frequencies after removing only V0V connections. We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them. …”
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Review article: Dynamical systems, algebraic topology and the climate sciences by M. Ghil, M. Ghil, M. Ghil, D. Sciamarella, D. Sciamarella, D. Sciamarella

“…The review is thus a trip leading from the applications of classical bifurcation theory to multiple possible climates to the tipping points associated with transitions from one type of climatic behavior to another in the presence of time-dependent forcing, deterministic as well as stochastic.…”
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Existence and multiplicity of solutions for second-order Dirichlet problems with nonlinear impulses by Ma Mantang, Ma Ruyun

“…We show the existence and multiplicity of solutions to the aforementioned problem for λ\lambda in a neighborhood of 1 by using degree theory and bifurcation theory.…”
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The role of coastal landforms in tourism development by mehran maghsudi

“…This creates an important and promising bridge between sustainability and bifurcation theory, one of the most important areas of systems analysis.…”
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Bifurcation Stability Analysis of the Synchronverter in a Microgrid by Juan Segundo Ramírez, Josué Hernández Ramírez, Nancy Visairo Cruz, Rafael Peña Gallardo

“…This work presents a stability analysis of a synchronverter-based system conducted through the bifurcation theory to expose its stability regions in a grid-connected configuration with an aggregate load model conformed by a ZIP model and an induction motor model. …”
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Nonlinear dynamic numerical analysis and prediction of complex system based on bivariate cycling time stochastic differential equation by Li Wang, Yuxi Wu, Jiping Xu, Huiyan Zhang, Xiaoyi Wang, Jiabin Yu, Qian Sun, Zhiyao Zhao

“…The time stochastic parameters and the prediction of cyanobacteria biomass is realized. The bifurcation theory and the central manifold theory were used to analyze the nonlinear dynamics of cyanobacteria growth with double nutrient cycling system, so that the conditions of cyanobacteria bloom and prediction of cyanobacteria blooms are achieved. …”
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Longitudinal dynamics, optimization and control of aircraft transition maneuver using aerodynamic vectoring by Adnan Maqsood

“…Specifically, Multiple Time Scales (MTS) method in conjunction with bifurcation theory is used to uncover the peculiar system behavior and to understand the steady transition dynamics further.…”
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Classification of bursting patterns: A tale of two ducks by Mathieu Desroches, John Rinzel, Serafim Rodrigues

“…In this review, we propose a comprehensive account of the main bursting classification systems that have been developed over the past 40 years, together with recent developments allowing us to extend these classifications. Based upon bifurcation theory and heavily reliant on timescale separation, these schemes take full advantage of the fast subsystem analysis, obtained when slow variables are frozen and considered as bifurcation parameters. …”
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A taxonomy of seizure dynamotypes by Maria Luisa Saggio, Dakota Crisp, Jared M Scott, Philippa Karoly, Levin Kuhlmann, Mitsuyoshi Nakatani, Tomohiko Murai, Matthias Dümpelmann, Andreas Schulze-Bonhage, Akio Ikeda, Mark Cook, Stephen V Gliske, Jack Lin, Christophe Bernard, Viktor Jirsa, William C Stacey

“…We introduce an organizing principle that leads to the first objective Taxonomy of Seizure Dynamics (TSD) based on bifurcation theory. The ‘dynamotype’ of a seizure is the dynamic composition that defines its observable characteristics, including how it starts, evolves and ends. …”
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Linear and nonlinear stability in nuclear reactors with delayed effects by Kostas Bučys, Donatas Švitra, Ramunė Vilkytė

“…In the nonlinear analysis the analytical expression of the solution is presented with the help of bifurcation theories. In the numerical experiment using the scientific simulation program “Model Maker” numerical Runge–Kutta IV series method asymptotically stable solution and a stable periodic solution has been received and compared to the stable periodic solution received in nonlinear analysis with the help of bifurcation theories.…”
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Formation of a Warped Nanomodular Surface Under Ion Bombardment. A Nanoscale Model of Surface Erosion by D. A. Kulikov, A. S. Rudy

“…The possibility of a ripple topography is demonstrated by means of bifurcations theory methods for dynamical systems with an infinite dimensional space of initial data. …”
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Formation of a Warped Nanomodular Surface Under Ion Bombardment. A Nanoscale Model of Surface Erosion by D. A. Kulikov, A. S. Rudy

“…The possibility of a ripple topography is demonstrated by means of bifurcations theory methods for dynamical systems with an infinite dimensional space of initial data. …”
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Multiple Solutions in Fluid Dynamics by L.-S. Yao

“…It compliments the current popular bifurcation theories by the fact that multiple solutions can exist on each stable bifurcation branch.…”
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The Study of the Development of the Hodgkin-Huxley (HH) Neuron Model by Ma Tianchi

“…It outlines the development of the most accurate but complex HH neuronal model and compares its strengths and weaknesses, introduces emerging developments in neurodynamics and bifurcation theories in terms of optimization, and argues that future developments will not be possible without the participation of multidisciplinary interdisciplinary field. …”
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Brief review of the development of theories of robustness, roughness and bifurcations of dynamic systems by Roman O. Omorov

“…Further research suggests the development of roughness and bifurcation theories for complex nonlinear dynamical systems.…”
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