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This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.
This article was published in the following journal.
Name: IEEE transactions on neural networks and learning systems
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A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.
An acquired disorder characterized by recurrent symptoms, referable to multiple organ systems, occurring in response to demonstrable exposure to many chemically unrelated compounds at doses below those established in the general population to cause harmful effects. (Cullen MR. The worker with multiple chemical sensitivities: an overview. Occup Med 1987;2(4):655-61)
An early embryonic developmental process of CHORDATES that is characterized by morphogenic movements of ECTODERM resulting in the formation of the NEURAL PLATE; the NEURAL CREST; and the NEURAL TUBE. Improper closure of the NEURAL GROOVE results in congenital NEURAL TUBE DEFECTS.
Bacteria that can survive and grow in the complete, or nearly complete absence of oxygen.
A benign tumor of the nervous system that may occur sporadically or in association with VON HIPPEL-LINDAU DISEASE. It accounts for approximately 2% of intracranial tumors, arising most frequently in the cerebellar hemispheres and vermis. Histologically, the tumors are composed of multiple capillary and sinusoidal channels lined with endothelial cells and clusters of lipid-laden pseudoxanthoma cells. Usually solitary, these tumors can be multiple and may also occur in the brain stem, spinal cord, retina, and supratentorial compartment. Cerebellar hemangioblastomas usually present in the third decade with INTRACRANIAL HYPERTENSION, and ataxia. (From DeVita et al., Cancer: Principles and Practice of Oncology, 5th ed, pp2071-2)