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Abstract: In this paper, a new complex-valued recurrent neural network (CVRNN) called complex-valued Zhang neural network (CVZNN) is proposed and simulated to solve the complex-valued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued time-varying matrix in an error-free manner. Moreover, by exploiting the design parameter , superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter involved (i.e., the situation with ). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion. [Copyright &y& Elsevier]

Abstract: In this paper, a competitive Lotka–Volterra system with three delays is investigated. By choosing the sum of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. [Copyright &y& Elsevier]