Article
Engineering, Mechanical
Miaomiao Xing, Zhuoqin Yang, Yong Chen
Summary: This study investigates the effect of temperature on the bursting discharge behavior of temperature-sensitive ion channels in neurons. The results show that an increase in temperature can promote the generation of bursting discharge, but eventually the bursting discharge phenomenon disappears. It is also found that even if the dynamic paths are consistent, the bursting discharge types and waveforms may be different, and vice versa.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics
Armengol Gasull, Anna Geyer, Victor Manosa
Summary: The paper addresses the persistence of traveling wave solutions (TWS) of a given PDE under small perturbations, proving that the persistent TWS are controlled by the zeroes of some Abelian integrals and applying the results to several famous PDEs.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Zhixiang Wang, Chun Zhang, Zuqin Ding, Qinsheng Bi
Summary: The aim of this paper is to reveal the dynamical mechanism of bursting oscillations in non-smooth dynamical systems, with a focus on the effects of period-doubling bifurcation and chaotic attractor. A modified fourth-order Chua's circuit is used to establish a dynamical system with non-smooth switching manifold and multiple scale variables. Subcritical non-smooth Hopf bifurcation, C-bifurcation, and period-doubling bifurcation are observed in the fast subsystem, along with chaotic attractors generated from period-doubling bifurcations. Eight typical bursting patterns are obtained through numerical simulations and bifurcation analysis, revealing their dynamical mechanism.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yi Lin, Wenbo Liu, Cheng Hang
Summary: It is important to construct physical hardware circuits that can reproduce abundant electrical activities of neurons for neuron-based engineering applications. In this study, a novel third-order nonautonomous memristive FitzHugh-Nagumo (FHN) neuron circuit is designed, which can generate abundant electrical activities with the use of a memristive-diode-bridge (MDB) emulator. The characteristics and dynamical behaviors of the circuit are analyzed through theoretical analysis, numerical simulation, and hardware experiments, revealing various non-chaotic firing activities.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Qinlong Wang, Yu'e Xiong, Wentao Huang, Pei Yu
Summary: In this paper, we investigate the bifurcations of local and global isolated periodic traveling waves in a single species population model. By utilizing the singular point quantity algorithm and numerical simulations, we discover that two large amplitude oscillations can coexist in a population model with density-dependent migrations and Allee effect.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Engineering, Mechanical
Linan Guan, Huaguang Gu, Zhiguo Zhao
Summary: The study demonstrates the modulation of resonance by I-h current in a bursting neuron model, which closely matches experimental observations. It reveals the modulation patterns of I-h current on the frequency and amplitude of resonance, as well as the mechanisms underlying subthreshold and suprathreshold resonance.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Youhua Qian, Danjin Zhang, Bingwen Lin
Summary: This study investigates the bursting oscillation mechanisms in systems with periodic excitation, analyzing different types of symmetric bursting oscillations and their bifurcation mechanisms through numerical simulations. The results show that these bursting oscillations exhibit symmetry in their patterns.
Article
Mathematics, Interdisciplinary Applications
Junting Gou, Xiaofang Zhang, Yibo Xia, Qinsheng Bi
Summary: This paper investigates the different types of bursting attractors that may appear in a vector field with Hopf bifurcation when periodic excitation is introduced. By treating the excitation term as a slow-varying bifurcation parameter, all possible equilibrium branches of the generalized autonomous system are derived. The trajectory of the system can visit four qualitatively different regions in the parameter space, leading to periodic symmetric oscillations, periodic symmetric mixed-mode oscillations, fold/Hopf/Hopf/fold and fold-Hopf/fold-Hopf bursting attractors.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Physics, Fluids & Plasmas
Suresh Kumarasamy, Malay Banerjee, Vaibhav Varshney, Manish Dev Shrimali, Nikolay V. Kuznetsov, Awadhesh Prasad
Summary: Hidden attractors, which are not associated with equilibria, are present in many nonlinear dynamical systems and are difficult to locate. This research letter presents the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. The study shows that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were conducted to demonstrate the existence of hidden attractors in these systems. The findings provide insights into the generation of hidden attractors in nonlinear dynamical systems.
Article
Mathematics, Interdisciplinary Applications
Yibo Xia, Shi Hua, Qinsheng Bi
Summary: The main purpose of this paper is to demonstrate that parts of the trajectory for chaotic bursting oscillations may oscillate according to different limit cycles, indicating the existence of orderly movement within chaos. By introducing a slow-varying controlling term, bursting oscillations can be observed, along with the presence of multiple periodic windows in the chaotic region.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Shaohui Yan, Zhenlong Song, Wanlin Shi, Weilong Zhao, Yu Ren, Xi Sun
Summary: An autonomous memristive circuit based on an active third-order generalized memristor is implemented, and the stability and complex dynamical behaviors of the system are analyzed using mathematical models. The feasibility of the theoretical analysis is verified through circuit experiments and numerical simulations.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Evdokiia Slepukhina, Irina Bashkirtseva, Lev Ryashko, Philipp Kuegler
Summary: Motivated by a biophysical problem related to neural activity, this study investigates a three-dimensional model with the Lukyanov-Shilnikov bifurcation. It reveals that additive white noise can induce a transition from spiking oscillations to bursting oscillations, accompanied by coherence resonance and subsequent chaos.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Danqi Feng, Yu Chen, Quanbao Ji
Summary: This study explores the numerical computation of Hopf bifurcation in the Chay model to illustrate the emergence of neuronal bursting induced by variations in the conductance of the Ca2+-sensitive IC+ channel. The results show that the formation and removal of various firing activities in this model are due to two subcritical Hopf bifurcations of equilibrium based on theoretical computation.
ELECTRONIC RESEARCH ARCHIVE
(2023)
Article
Mathematics
Bo Lu, Xiaofang Jiang
Summary: The paper presents the characteristics and modeling approach of intrinsic bursting neurons, demonstrating the effectiveness of projection reduction and bifurcation analysis in revealing the intrinsic features of the simplified model and its practicality in neuronal modeling.
ELECTRONIC RESEARCH ARCHIVE
(2023)
Article
Engineering, Mechanical
Feng Zhao, Xindong Ma, Shuqian Cao
Summary: This paper focuses on the periodic complex bursting dynamics in a hybrid Rayleigh-Van der Pol-Duffing oscillator driven by external and parametric slow-changing excitations. Different bursting modes are proposed and analyzed, and the theoretical analysis results are validated through numerical simulations. The study reveals the dependence of bursting patterns on system parameters and the influence of different stable attractors on the manifolds of the excited state oscillations.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Krishna Pusuluri, Sunitha Basodi, Andrey Shilnikov
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2020)
Review
Mathematics, Applied
J. Collens, K. Pusuluri, A. Kelley, D. Knapper, T. Xing, S. Basodi, D. Alacam, A. L. Shilnikov
Article
Computer Science, Artificial Intelligence
Matteo Lodi, Andrey L. Shilnikov, Marco Storace
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2020)
Article
Mathematics, Applied
K. Pusuluri, H. G. E. Meijer, A. L. Shilnikov
Summary: This study presents a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. By combining traditional parameter continuation methods with a newly developed technique, specific codimension-two bifurcations origins and patterns regions of chaotic and simple dynamics in the classical model. Computational reconstructions of key bifurcation structures and their spatial organization in both 2D and 3D parameter spaces are shown.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Tingli Xing, Krishna Pusuluri, Andrey L. Shilnikov
Summary: Using Poincare return maps, the study reveals an intricate order of subsequent homoclinic bifurcations near the primary figure-8 connection of the Shilnikov saddle-focus in systems with reflection symmetry. The admissible shapes of bifurcation curves in parameter space are shown to have universal scalability ratio and organization for higher-order homoclinic bifurcations. Two applications, including a smooth adaptation of the Chua circuit and a 3D normal form, illustrate the theory of similar dynamics due to the Shilnikov saddle-foci.
Article
Mathematics, Applied
Natalia B. Janson, Christopher J. Marsden
Summary: This study examines nonlinear systems with delay and proposes a hypothesis for qualitatively predicting delay-induced effects, which is verified by exploring a specific type of system. The research reveals that delay-induced reorganization of manifolds after homoclinic bifurcations allows the system to visit vicinities of all local minima without barriers.
Article
Mathematics, Applied
James J. Scully, Alexander B. Neiman, Andrey L. Shilnikov
Summary: This study focuses on qualitative and quantitative characterization of chaotic systems using symbolic description, demonstrating effective measures of complexity for characterizing chaos and detecting stability windows. The utility of symbolic dynamics is showcased for simulating chaos properties with a fidelity test.
Editorial Material
Mathematics, Applied
Sergey Gonchenko, Alexey Kazakov, Dmitry Turaev, Andrey L. Shilnikov
Article
Physics, Fluids & Plasmas
Joseph D. Taylor, Ashok S. Chauhan, John T. Taylor, Andrey L. Shilnikov, Alain Nogaret
Summary: Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. The study finds that at low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape probability becomes comparable to the intrabasin hopping probability, the lifetime of attractors is given by a detailed balance where the less coherent attractors act as a sink for the more coherent ones. Assigning pseudoactivation energies to limit cycle attractors provides a useful metric for evaluating the resilience of biological rhythms to perturbations.
Article
Physics, Fluids & Plasmas
V. Baruzzi, M. Lodi, M. Storace, A. Shilnikov
Summary: This paper introduces a method for designing CPG models capable of demonstrating biologically plausible gait transitions, and successfully reproduces three out of four standard quadruped gaits through a case study.
Article
Mathematics, Interdisciplinary Applications
Aaron Kelley, Andrey Shilnikov
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
(2020)
Article
Mathematics, Applied
Semyon Malykh, Yuliya Bakhanova, Alexey Kazakov, Krishna Pusuluri, Andrey Shilnikov
Article
Physics, Fluids & Plasmas
V. Baruzzi, M. Lodi, M. Storace, A. Shilnikov
Proceedings Paper
Engineering, Electrical & Electronic
Matteo Lodi, Andrey Shilnikov, Marco Storace
2019 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS)
(2019)
Proceedings Paper
Engineering, Electrical & Electronic
Matteo Lodi, Andrey Shilnikov, Marco Storace
2018 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS)
(2018)
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
