In this paper, the effect of neuronal gain in discrete delayed neural network model is investigated. It is observed that such neural networks become highly chaotic due to the presence of high neuronal gain. On the basis of the largest Lyapunov exponent and largest eigenvalue of Jacobian matrix, chaos analysis has been done. Finally, some numerical simulations are presented to justify our results.
Network analysis is performed on a 14 species food web model of the ecosystem occupying a mudflat on a partly reclaimed island of the Sundarban mangrove ecosystem. The results demonstrate a dramatic difference between this heavily impacted mangrove ecosystem in its modes of primary and secondary production and its diminished role of detritus vis-a-vis its less disturbed counterparts. Unlike most benthic mangrove systems, the Sundarban bottom community receives a large contribution from the phytoplankton populations. In this system herbivory and detritivory are virtually equal, in contrast to the usual herbivory:detritivory ratio of 1:5. Anthropogenic impacts have changed the physiography of this system so as to increase the relative importance of zooplankton and meiobenthos as herbivores. Although a slight degree of omnivory is exhibited by the populations of larger organisms, all flows of each integer of trophic length into a food chain may be aggregated that represents the underlying trophic status of the starting food web. Only a small number of pathways of recycle can be identified (31), and the Finn cycling index for this system is quite low (8.4%). Litterfall comprises only 16% of the total system input, which is very little in comparison with most mangrove systems. Pathway redundancy is rather high in this ecosystem, indicating that the surviving system is probably highly resilient to further perturbations, as one might expect for a highly impacted system.
Problem statement: Artificial Neural Network (ANN) are simple models to mimic some essential features of the complex central nervous system. ANN models are realistic due to their inherent stochastic nature of neural computation and strong synchronicity. Different ANN models are associated with directed and signed graphs. The present study proceeded by relaxing certain simplifying assumptions in the ANN model. Approach: It was assumed that the connected graph associated with the ANN is a multipartite directed graph whose connection comprising of four blocks and two blocks are either both symmetric or both anti symmetric. The convergence of such network was studied in the present research with the help of Lyapunov functional. Results: Attractors (fixed points) of such ANN and also limit cycles of different orders are investigated. Bounds of transient length of the neural network were also calculated. Numerical simulation in support of the results was also depicted. Conclusion: It was shown that under synchronous updating rule such networks converge to a fixed point or to a limit cycle of period 2 or 4. The bound of transient length was discussed. Conclusions were drawn from the simulation studies carried out in support of the results
A distributed delay model of a class of three-neuron network has been investigated. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic solution occurs for each point of such interval. The orbital stability of such bifurcating periodic solution at the extreme points of the interval is ascertained. Lastly global bifurcation aspect of such periodic solutions is studied. The results are illustrated by numerical simulations.
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