The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.
A mathematical model of artificial neural networks with hysteresis is formulated using neutral delay differential equations. Hysteresis modifies the systems such that they cannot produce unique output for any given input, rather output is produced based on the past history of the system. Motivated by the applications of complex valued neural networks in artificial neural networks, we studied the global dynamics of complex valued neural network with hysteresis. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the neural delay. In this paper continuous hysteresis neuron model has been used to arrive at the sufficient condition for global exponential stability of a unique equilibrium. The hypothetical insight has been successfully applied and verified using relevant numerical examples.
Abstract. The present paper is devoted to an analytical study of a three species ecological model in which a predator is preying on the other two species which are mutually helping each other. In addition to that, all the three species are provided with an alternate food. The model is characterized by a set of first order non-linear differential equations. All the possible equilibrium points of the model have been derived and the local and global stability for the positive equilibrium point is discussed and supported by the numerical simulation using the MATLAB.
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