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Discrete-time nonlinear systems modeling
International Conference on Acoustics, Speech, and Signal Processing, 2002Systems theory and some canonical representations are introduced for a class of nonlinear systems. Techniques are devised to identify, synthesize, and model such systems and their signals. Nonlinear systems theory is introduced at a fundamental level.
R.D. DeGroat, L.R. Hunt, D.A. Linebarger
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2015
In this chapter, a theory for nonlinear discrete systems is reviewed. The local and global theory of stability and bifurcation for nonlinear discrete systems is presented. The stability switching and bifurcation on specific eigenvectors of the linearized system at fixed points under a specific period are discussed.
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In this chapter, a theory for nonlinear discrete systems is reviewed. The local and global theory of stability and bifurcation for nonlinear discrete systems is presented. The stability switching and bifurcation on specific eigenvectors of the linearized system at fixed points under a specific period are discussed.
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Quartic Nonlinear Discrete Systems
2020In this Chapter, the stability and bifurcation of the quartic nonlinear discrete systems will be ...
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Nichtlineare zeitdiskrete Systeme / Nonlinear discrete-time systems
auto, 1988Using simple nonlinear discrete-time first order systems the significant differences to the response of linear discrete-time systems, but also to the response of nonlinear continuous-time systems are demonstrated. The phenomena bifurcation and chaos as well as the principle difficulties with the simulation of the chaotic behaviour are described.
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Quadratic Nonlinear Discrete Systems
2020In this Chapter, the global stability and bifurcation of quadratic nonlinear discrete systems are discussed. Appearing and switching bifurcations of simple period-1 fixed-points are discussed. Period-1 and period-2 bifurcation trees with global stability are presented for forward and backward quadratic discrete systems.
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Discrete and Continuous Nonlinear Schrödinger Systems
2003In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of ...
M. J. ABLOWITZ +2 more
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Local Stabilization of Discrete-Time Nonlinear Systems
IEEE Transactions on Fuzzy Systems, 2022This paper considers local stability analysis and local stabilization of discrete-time nonlinear systems represented by Takagi-Sugeno fuzzy models. Conditions are established using Lyapunov functions and controller gains that depend also on past samples.
Zsofia Lendek, Jimmy Lauber
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Cubic Nonlinear Discrete Systems
2020In this Chapter, the stability and stability switching of fixed-points in cubic polynomial discrete systems are discussed. As in Luo (2019), the monotonic upper-saddle-node and lower-saddle-node appearing and switching bifurcations are discussed and the third-order monotonic sink and source switching bifurcations are discussed as well.
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Nonlinear interactions in discrete systems
The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003., 2004We report our experimental and numerical investigation of nonlinear beam interactions in discrete waveguide arrays. We investigated the case of two parallel, copolarized beams interacting for different power levels and varying initial phase.
J. Meier +5 more
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Multipulses in discrete Hamiltonian nonlinear systems
Physical Review E, 2001In this work, the behavior of multipulses in discrete Hamiltonian nonlinear systems is investigated. The discrete nonlinear Schrödinger equation is used as the benchmark system for this study. A singular perturbation methodology as well as a variational approach are implemented in order to identify the dominant factors in the discrete problem.
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