Article
Mathematics, Applied
George Datseris, Kalel Luiz Rossi, Alexandre Wagemakers
Summary: This paragraph describes the existence of coexisting stable states called attractors in dynamical systems used to model power grids, the brain, and other physical systems. Global stability analysis is a powerful tool to understand these systems and predict transitions between stable states. The authors present an improved framework that allows for efficient and convenient global stability analysis over a parameter range, going beyond local stability analysis offered by other frameworks.
Article
Mathematics, Applied
Nitha P. C. Niralda, Sunil Mathew, Nicolae Adrian Secelean
Summary: This paper explores the concept of self similarity in fractal geometry and the use of Iterated Function Systems (IFS) to generate fractals. Different variants of IFSs and boundary concepts are discussed in relation to self similar sets. The characterization of self similar sets using the Hausdorff measure of boundaries is also examined towards the end.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Review
Physics, Multidisciplinary
D. J. W. Simpson
Summary: This paper reviews 20 "Hopf-like" bifurcations in two-dimensional ODE systems with state-dependent switching rules, including boundary equilibrium bifurcations, the collision or change of stability of equilibria or folds on switching manifolds, and limit cycle creation via hysteresis or time delay. Each bifurcation is quantitatively analyzed, and complete derivations based on asymptotic expansions of Poincare maps are provided.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2022)
Article
Engineering, Multidisciplinary
Megan Morrison, J. Nathan Kutz
Summary: This study develops a mathematical framework for controlling nonlinear, networked dynamical systems, using dimensionality reduction, bifurcation theory, and model discovery tools to find low-dimensional subspaces for feed-forward control. By leveraging the fact that high-dimensional networked systems have many fixed points, control signals can be computed to move the system between any pair of fixed points. The approach involves fitting a nonlinear dynamical system to a low-rank subspace with the SINDy algorithm, then using bifurcation theory to identify constant control signals for achieving desired outcomes.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Hao Zhang, Han Ren, Donggang Cui
Summary: This paper thoroughly investigates the evolution of three types of border collision bifurcations in a high-order single-inductor double-output DC-DC converter under one-cycle control. The study reveals the underlying mechanisms of complicated nonstandard bifurcations and provides parameter boundaries for design guidance.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Nazanin Zandi-Mehran, Fahimeh Nazarimehr, Karthikeyan Rajagopal, Dibakar Ghosh, Sajad Jafari, Guanrong Chen
Summary: This paper presents FFT bifurcation as a tool for investigating complex dynamics and discusses various systems with different properties in both discrete-time and continuous-time systems. The results of FFT bifurcation diagrams are compared with conventional bifurcation diagrams, showing interesting findings.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
S. Kamyar Tavakoli, Andre Longtin
Summary: The study explores the influence of multiple delays on the dynamics of first-order nonlinear differential equations, finding that proper distribution of delays can induce stability or chaos. Narrow spacing between delays leads to chaotic behavior, while lower density of delays enables stable periodic or fixed point behavior.
Article
Mathematics, Applied
Ugo Merlone, Irene Alfarone
Summary: The music labor market is highly competitive, with an oversupply of professionals and employment uncertainty, leading many musicians to switch to non-musical careers. This study proposes a dynamic model that incorporates career choices influenced by other musicians' decisions, and analyzes the attractors and boundaries of cycles. The model accurately reproduces musicians' employment situations and sheds light on their career sustainability choices.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Jaume Ojer, Alvaro G. Lopez, Javier Used, Miguel A. F. Sanjuan
Summary: We reproduce the phenomenon of chemotaxis using a hybrid random walk model on a two-dimensional lattice. The dynamics of the chemoattractant is modelled using a partial differential equation, while the cell is treated discretely and influenced by concentration gradients. The bias towards higher chemical concentrations is determined by a stochastic process, which is controlled by a single parameter related to the attractiveness of the source and its efficiency in cellular capture. The model has been thoroughly analyzed in terms of parameter space and the efficiency of cellular capture is illustrated using stochastic basins of attraction.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
I. Sushko, V. Avrutin, L. Gardini
Summary: In this paper, the bifurcation structure of the Lozi map, a 2D piecewise linear continuous two-parameter map, is investigated and compared to the 2D border collision normal form. By analyzing the boundaries of the largest periodicity regions related to cycles with rotation number 1/n (n=3), the bifurcation structure of the Lozi map is incorporated into the 2D border collision normal form. Both maps exhibit intricate bifurcation structures near the center bifurcation boundary of the stability domain of the fixed point due to their conservative nature.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
M. A. Navascues
Summary: This study introduces the concept of quasi-fixed points in non-autonomous discrete dynamical systems in metric spaces and proves their role similar to fixed points in autonomous systems. It also presents sufficient conditions for convergence, including reordering of maps and forward/backward directions, and extends the Banach fixed point theorems.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Developmental Biology
Simon L. Freedman, Bingxian Xu, Sidhartha Goyal, Madhav Mani
Summary: This study presents a mathematical formalism to analyze single-cell transcriptomic data from a dynamical systems perspective. It reveals the multistability of cellular differentiation and identifies the low-dimensional phase plane in gene expression space. The study also uncovers novel genetic players crucial for neutrophil differentiation.
Article
Physics, Mathematical
Maximilian Engel, Christian Kuehn
Summary: The discussion in the mathematical physics community has focused on defining isochrons for stochastic oscillations, comparing the approach of finding stochastic isochrons as equal expected return time sections with considering eigenfunctions of the backward Kolmogorov operator.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
BahaaAlDeen M. AboAlNaga, Lobna A. Said, Ahmed H. Madian, Ahmed G. Radwan
Summary: This paper explores the fractal-like behavior of the complex form of Gaussian chaotic map and the ability of digital architectures to mimic it, with the hope that a digital realization of fractals may also be achieved. The study involves analyzing the Gauss map in terms of its bifurcation behavior, time waveform plots, Lyapunov exponent, and attractor performance through parameter variation. Additionally, FPGA implementation of the fractal behavior is discussed, leading to an experimentally displayed fractal entity.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Mechanical
B. E. Saunders, R. Vasconcellos, R. J. Kuether, A. Abdelkefi
Summary: This work investigates the interaction between contact/impact nonlinearity and geometric cubic nonlinearity in an oscillator system, focusing on bifurcation behavior and secondary resonances. It is found that the nonlinearities do not destructively interfere and have different effects on super-and sub-harmonic resonances. Contact nonlinearity affects superharmonic resonance more, while cubic nonlinearity influences subharmonic resonance and tends to lead to multistable behavior. Perturbation theory helps determine when cubic nonlinearity dominates over contact nonlinearity.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Physics, Multidisciplinary
Kenji Yamazaki, Yosuke Maehara, Kazutoshi Gohara
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
(2018)
Article
Physics, Applied
Kenji Yamazaki, Yosuke Maehara, Ryo Kitajima, Yuta Fukami, Kazutoshi Gohara
APPLIED PHYSICS EXPRESS
(2018)
Article
Engineering, Electrical & Electronic
Sota Takahashi, Shuto Muramatsu, Jun Nishikawa, Kazuo Satoh, Shuichi Murakami, Takashi Tateno
IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING
(2019)
Article
Chemistry, Physical
Kenji Yamazaki, Yosuke Maehara, Chi-Cheng Lee, Jun Yoshinobu, Taisuke Ozaki, Kazutoshi Gohara
JOURNAL OF PHYSICAL CHEMISTRY C
(2018)
Review
Chemistry, Multidisciplinary
Yuji Yamamoto, Akifumi Kijima, Motoki Okumura, Keiko Yokoyama, Kazutoshi Gohara
APPLIED SCIENCES-BASEL
(2019)
Article
Chemistry, Physical
Yosuke Maehara, Kenji Yamazaki, Kazutoshi Gohara
Article
Neurosciences
Shuto Muramatsu, Masato Toda, Jun Nishikawa, Takashi Tateno
Article
Biology
Tsutomu Uchida, Maho Furukawa, Takahiro Kikawada, Kenji Yamazaki, Kazutoshi Gohara
Article
Chemistry, Physical
Ryo Takahata, Seiji Yamazoe, Yosuke Maehara, Kenji Yamazaki, Shinjiro Takano, Wataru Kurashige, Yuichi Negishi, Kazutoshi Gohara, Tatsuya Tsukuda
JOURNAL OF PHYSICAL CHEMISTRY C
(2020)
Article
Chemistry, Multidisciplinary
Tsutomu Uchida, Hiroshi Miyoshi, Ren Sugibuchi, Akio Suzuta, Kenji Yamazaki, Kazutoshi Gohara
FRONTIERS IN CHEMISTRY
(2020)
Article
Engineering, Electrical & Electronic
Shunsuke Sugai, Hisaya Higuchi, Jun Nishikawa, Kazuo Satoh, Shuichi Murakami, Takashi Tateno
IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING
(2020)
Article
Engineering, Electrical & Electronic
Takumi Kuwano, Hiroki Kaneta, Jun Nishikawa, Kazuo Satoh, Shuichi Murakami, Takashi Tateno
IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING
(2020)
Article
Chemistry, Physical
Ryo Sugimoto, Yuhiro Segawa, Akio Suzuta, Yuji Kunisada, Tsutomu Uchida, Kenji Yamazaki, Kazutoshi Gohara
Summary: Nitrogen (N) enhances the stability of single Pt atoms on graphene, as Pt and N atoms prefer adsorption near the step edge. Experimental and theoretical studies confirm that N strengthens the bond between Pt and C, increasing the stability of single Pt atoms on graphene.
JOURNAL OF PHYSICAL CHEMISTRY C
(2021)
Article
Chemistry, Multidisciplinary
Yuhiro Segawa, Kenji Yamazaki, Jun Yamasaki, Kazutoshi Gohara
Summary: A new method for measuring the 3D atomic structure of free-standing graphene ripples using TEM is proposed and experimentally validated. The specimen in the experiment was found to be moving upward, and the ripple was approximated as a composite of sinusoidal waves while measuring the time dependence of its height and lateral size.
Article
Geography, Physical
Tsutomu Uchida, Maho Furukawa, Takahiro Kikawada, Kenji Yamazaki, Kazutoshi Gohara
BULLETIN OF GLACIOLOGICAL RESEARCH
(2019)