Periodic and Solitary-Wave Solutions for a Variant of the K(3,2) Equation by Jiangbo Zhou, Lixin Tian

“…We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3,2) equation. …”
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Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type by W. Weera, P. Niamsup

“…We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. …”
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Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise by Xiaoyao Jia, Xiaoquan Ding

“…Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. …”
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Fractional Order Models of Industrial Pneumatic Controllers by Abolhassan Razminia, Dumitru Baleanu

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Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey–Stewartson System by Tianyong Han, Jiajin Wen, Zhao Li

“…On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. …”
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Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models by Jianping Shi, Jibin Li

“…We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. …”
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Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems by Rui Qu, Shaolong Li

“…The main purpose of this paper is to investigate the mechanism of sliding phenomenon in Filippov (nonsmooth) dynamical systems by attractor analysis and vector analysis. …”
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A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results by Yan Zhao, Weiguo Zhang

“…By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. …”
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An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game by Ikjyot Singh Kohli, Michael C. Haslam

“…We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. …”
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Nonlinear stochastic Markov processes and modeling uncertainty in populations by H.Thomas Banks, Shuhua Hu

“…We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations.These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. …”
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New Exact Solitary Wave Solutions of a Coupled Nonlinear Wave Equation by XiaoHua Liu, CaiXia He

“…By using the theory of planar dynamical systems to a coupled nonlinear wave equation, the existence of bell-shaped solitary wave solutions, kink-shaped solitary wave solutions, and periodic wave solutions is obtained. …”
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Peakon, Cuspon, Compacton, and Loop Solutions of a Three-Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion by Haixia Zhao, Lijing Qiao, Shengqiang Tang

“…Based on the method of dynamical systems, the 3DKP(3,2) equation is shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, compacton, and loop solutions. …”
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Travelling wave solutions for higher-order wave equations of KDV type (III) by Jibin Li, Weigou Rui, Yao Long, Bin He

“…By using the theory of planar dynamical systems to the travellingwave equation of a higher order nonlinear wave equations of KdV type, theexistence of smooth solitary wave, kink wave and anti-kink wave solutions anduncountably infinite many smooth and non-smooth periodic wave solutions areproved. …”
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Rate Estimation of Identical Synchronization by Designing Controllers by Mitul Islam, Bipul Islam, Nurul Islam

“…This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. …”
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Exact Traveling Wave Solutions and Bifurcation of a Generalized (3+1)-Dimensional Time-Fractional Camassa-Holm-Kadomtsev-Petviashvili Equation by Zhigang Liu, Kelei Zhang, Mengyuan Li

“…Furthermore, the phase portraits of the dynamical system and the remarkable features of the solutions are demonstrated via interesting figures.…”
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Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations by Shaoyong Li, Zhengrong Liu

“…We investigate the traveling wave solutions for the ZK-BBM() equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. …”
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Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems by Jeong Ryeol Choi

“…An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. …”
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Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay by S. J. Sadati, D. Baleanu, A. Ranjbar, R. Ghaderi, T. Abdeljawad (Maraaba)

“…Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. …”
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Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators by Gerold Baier, Sven Sahle

“…We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. …”
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Spectral study of COVID-19 pandemic in Japan: The dependence of spectral gradient on the population size of the community. by Ayako Sumi, Masayuki Koyama, Manato Katagiri, Norio Ohtomo

“…The results confirm that the power spectral densities (PSDs) of the data from each prefecture show exponential characteristics, which are universally observed in the PSDs of time series generated by nonlinear dynamical systems, such as the susceptible/exposed/infectious/recovered (SEIR) epidemic model. …”
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