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Horikawa Y. Effects of asymmetry in an output function on the pinning of rotating waves in a ring neural oscillator with asymmetric bidirectional coupling and self-coupling. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2014.03.036] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Abstract
We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term and additive independent white noise at each node. We prove the existence of a compact global random attractor within the set of tempered random bounded sets. An interesting feature of this is that, even though the spatial domain is unbounded and the solution operator is not smoothing or compact, pulled back bounded sets of initial data converge under the forward flow to a random compact invariant set.
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Affiliation(s)
- PETER W. BATES
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
| | - HANNELORE LISEI
- Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Str. Kogalniceanu Nr. 1, RO — 400084 Cluj-Napoca, Romania
| | - KENING LU
- Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
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Setti G, Thiran P, Serpico C. An approach to information propagation in 1-D cellular neural networks. II. Global propagation. ACTA ACUST UNITED AC 1998. [DOI: 10.1109/81.704820] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Thiran P, Setti G, Hasler M. An approach to information propagation in 1-D cellular neural networks-Part I: Local diffusion. ACTA ACUST UNITED AC 1998. [DOI: 10.1109/81.704819] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Chow SN, Mallet-Paret J. Pattern formation and spatial chaos in lattice dynamical systems. I. ACTA ACUST UNITED AC 1995. [DOI: 10.1109/81.473583] [Citation(s) in RCA: 150] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Thiran P, Crounse K, Chua L, Hasler M. Pattern formation properties of autonomous Cellular Neural Networks. ACTA ACUST UNITED AC 1995. [DOI: 10.1109/81.473585] [Citation(s) in RCA: 91] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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