Nonlinear dynamical systems
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems Open
Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a nov…
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Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators Open
A chimera state is a spatio-temporal pattern in a network of identical\ncoupled oscillators in which synchronous and asynchronous oscillation coexist.\nThis state of broken symmetry, which usually coexists with a stable spatially\nsymmetri…
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Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction Open
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be …
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Synchronization and Dynamic Consensus of Heterogeneous Networked Systems Open
We present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs. Heterogeneous systems may have totally different dynamical models, albeit of th…
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Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue Open
Multistability refers to the coexistence of different stable states in nonlinear dynamical systems. This phenomenon has been observed in laboratory experiments and in nature. In this introduction, we briefly introduce the classes of dynami…
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Clustering as a Prerequisite for Chimera States in Globally Coupled Systems Open
The coexistence of coherently and incoherently oscillating parts in a system of identical oscillators with symmetrical coupling, i.e., a chimera state, is even observable with uniform global coupling. We address the question of the prerequ…
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Self-Triggered Model Predictive Control for Nonlinear Input-Affine Dynamical Systems via Adaptive Control Samples Selection Open
In this paper, we propose a self-triggered formulation of Model Predictive Control for continuous-time nonlinear input-affine networked control systems. Our control method specifies not only when to execute control tasks but also provides …
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Multibody interactions and nonlinear consensus dynamics on networked systems Open
Multibody interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups…
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Nonlinearity of local dynamics promotes multi-chimeras Open
Chimera states are complex spatio-temporal patterns in which domains of synchronous and asynchronous dynamics coexist in coupled systems of oscillators. We examine how the character of the individual elements influences chimera states by s…
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Long‐Time Predictive Modeling of Nonlinear Dynamical Systems Using Neural Networks Open
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and t…
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Networkcontrology Open
An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control…
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Sparse Identification of Nonlinear Dynamics with Control (SINDYc) Open
Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using regress…
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Chimera states in two-dimensional networks of locally coupled oscillators Open
Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse…
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Impact of symmetry breaking in networks of globally coupled oscillators Open
We analyze the consequences of symmetry breaking in the coupling in a network of globally coupled identical Stuart-Landau oscillators. We observe that symmetry breaking leads to increased disorderliness in the dynamical behavior of oscilla…
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Dynamical analysis of long-wave phenomena for the nonlinear conformable space-time fractional (2+1)-dimensional AKNS equation in water wave mechanics Open
The main intension of this paper is to extract new and further general analytical wave solutions to the (2 + 1)-dimensional fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation in the sense of conformable derivative by implementing the ad…
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Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems Open
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode deco…
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Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media Open
We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transiti…
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Topological Causality in Dynamical Systems Open
Determination of causal relations among observables is of fundamental interest in many fields dealing with complex systems. Since nonlinear systems generically behave as wholes, classical notions of causality assuming separability of subsy…
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Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems Open
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing nonlinearizable systems with multiple coexisting steady states have been unavailable. In this paper, we r…
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An Integrated Learning and Filtering Approach for Fault Diagnosis of a Class of Nonlinear Dynamical Systems Open
This paper develops an integrated filtering and adaptive approximation-based approach for fault diagnosis of process and sensor faults in a class of continuous-time nonlinear systems with modeling uncertainties and measurement noise. The p…
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Soliton solutions for the Zoomeron model applying three analytical techniques Open
The Zoomeron equation is used in various categories of soliton with unique characteristics that arise in different physical phenomena, such as fluid dynamics, laser physics, and nonlinear optics. To achieve soliton solutions for the Zoomer…
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Multidimensional approximation of nonlinear dynamical systems Open
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system ident…
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New soliton wave structures of nonlinear (4 + 1)-dimensional Fokas dynamical model by using different methods Open
The physics of the (4 + 1)-dimensional Fokas equation follows necessarily from the physical nature of the Kadomtsev–Petviashvili and Davey-Stewartson equations in wave theory. In this article, we consider the nonlinear (4+1)-dimensional Fo…
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A Generalized Coherence Framework for Detecting and Characterizing Nonlinear Interactions in the Nervous System Open
This novel framework 1) unveils the nonlinear neural dynamics in a more complete way than the existing coherence measures, and 2) is more suitable for estimating the input-output relation regarding both phase and amplitude compared to phas…
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Statistical inference for dynamical systems: A review Open
The topic of statistical inference for dynamical systems has been studied widely across several fields. In this survey we focus on methods related to parameter estimation for nonlinear dynamical systems. Our objective is to place results a…
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Chaos synchronization of nonlinear dynamical systems via a novel analytical approach Open
This paper deals with the synchronization between two non-identical 4-D hyperchaotic systems. The nonlinear control technique is used for synchronization. The stability analysis of the error dynamics system is done by (i) Lyapunov's second…
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Numerical design of Luenberger observers for nonlinear systems Open
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Nonlinear dynamics as an engine of computation Open
Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-bas…
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Attitude and Altitude Control of Unmanned Aerial-Underwater Vehicle Based on Incremental Nonlinear Dynamic Inversion Open
A vehicle able to navigate both in the air and underwater is referred to an unmanned aerial-underwater vehicle (UAUV). Aiming at the attitude and altitude control of UAUVs, an incremental dynamic inverse control (INDI) method with second-o…
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Prediction and classification in equation-free collective motion dynamics Open
Modeling the complex collective behavior is a challenging issue in several material and life sciences. The collective motion has been usually modeled by simple interaction rules and explained by global statistics. However, it remains diffi…