|
This article is cited in 4 scientific papers (total in 4 papers)
Dissipative and Hamiltonian Systems with Chaotic Behavior: An Analytic Approach
A. K. Abramyan, S. A. Vakulenko Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Abstract:
Some classes of dissipative and Hamiltonian distributed systems are described. The dynamics of these systems is effectively reduced to finite-dimensional dynamics which can be unboundedly complex in a sense. Yarying the parameters of these systems, we can obtain an arbitrary (to within the orbital topological equivalence) structurally stable attractor in the dissipative case and an arbitrary polynomial weakly integrable Hamiltonian in the conservative case. As examples, we consider Hopfield neural networks and some reaction-diffusion systems in the dissipative case and a nonlinear string in the Hamiltonian case.
Received: 24.05.2001
Citation:
A. K. Abramyan, S. A. Vakulenko, “Dissipative and Hamiltonian Systems with Chaotic Behavior: An Analytic Approach”, TMF, 130:2 (2002), 287–300; Theoret. and Math. Phys., 130:2 (2002), 245–255
Linking options:
https://www.mathnet.ru/eng/tmf303https://doi.org/10.4213/tmf303 https://www.mathnet.ru/eng/tmf/v130/i2/p287
|
Statistics & downloads: |
Abstract page: | 434 | Full-text PDF : | 219 | References: | 48 | First page: | 1 |
|