Journal of Nonlinear Mathematical Physics最新文献

We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg–Landau equation (CQGLE). Solutions in the closed analytical form in the spectral domain have the shape of Rayleigh–Jeans distribution for a positive (normal) dispersion. The DS parametric space forms a two-dimensional (or three-dimensional for the complex quintic nonlinearity) master diagram connecting the DS energy and a universal parameter formed by the ratio of four real and imaginary coefficients for dissipative and non-dissipative terms in CQGLE. The concept of dissipative soliton resonance (DSR) is formulated in terms of the master diagram, and the main signatures of transition to DSR are demonstrated and experimentally verified. We show a close analogy between DS and incoherent (semicoherent) solitons with an ensemble of quasi-particles confined by a collective potential. It allows applying the thermodynamical approach to DS and deriving the conditions for the DS energy scalability.

This paper considers the adaptive fuzzy control of fractional-order nonlinear networked control systems subjected to network-induced input delay and data loss. To approximate unknown functions, fuzzy logic systems are employed. Furthermore, the Pade approximation method and an intermediate variable are introduced to eliminate the impact of input delay, and an adaptive fuzzy controller is designed using backstepping technology. Based on fractional-order Lyapunov stability theory, the proposed method can ensure that all signals are uniformly ultimately bounded, and the tracking error can converge to a small region of the origin. Two simulation examples are provided to verify the viability of the control method.

This paper is concerned with the bifurcation of the traveling wave solutions, as well as the dynamical behaviors and physical property of the soliton solutions of the (2+1)-dimensional extended Vakhnenko–Parkes (eVP) equation. Firstly, based on the traveling wave transformation, the planar dynamical system corresponding to the (2+1)-dimensional eVP equation is derived, and then the singularity type and trajectory map of this system are obtained and analyzed. Based on the bifurcation of this system, the analytical expression for the periodic wave solution is given and shown graphically. Secondly, the N-soliton solutions are obtained via the bilinear method, and some important physical quantities and asymptotic analysis of one-soliton and two-soliton solutions are discussed. The results obtained in this paper might be useful for understanding the propagation of high-frequency waves.

The Duffing Chaos System can detect weak signals that are obscured by Gaussian noise because it is sensitive to specific signal functions and can withstand noise. In this paper, we investigate the use of intermittent chaotic phenomena in fractional-order incommensurate Duffing chaotic systems for weak signal detection. This new intermittent chaotic state has not appeared in integer-order Duffing systems before, so this phenomenon reflects the superiority of fractional-order Duffing systems. We start by giving the incommensurate fractional-order Duffing system’s weak signal detection model. Then design a time series-based judgment method that successfully separates chaotic, intermittent chaotic, and limit cycle states. Finally, the intermittent chaotic of fractional-order detection system is used to determine the amplitude and frequency of the weak signals to calculate the detection performance. The results show that the weak signal can be detected at a maximum signal-to-noise ratio of (-)13.26 dB for single-detection oscillator amplitude detection. When detecting the frequency, a single-detection oscillator can detect the frequency range of 1050 rad/s, proving that the fractional-order chaos detection system is better than the integer-order chaos detection system.