We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of $$u_i \left( {t + 1} \right) = ku_i \left( t \right) + \Delta t\left( {...We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of $$u_i \left( {t + 1} \right) = ku_i \left( t \right) + \Delta t\left( {\sum\limits_{j = 1}^n {a_{ij} v_j \left( t \right) + a_i } } \right), i = 1,2, \cdots ,n,$$ , where the input-output function is defined as a generalized sigmoid function, such asv i =2/π arctan(π/2μiμi), $v_i = \frac{2}{\pi }arctan\left( {\frac{\pi }{2}\mu _i u_i } \right)$ and $v_i = \frac{1}{{1 + e^{ - u_i /\varepsilon } }},$ , etc. Numerical simulations are also provided to demonstrate the theoretical results.展开更多
基金This work was supported by the National Key Basic Research Special Found (Grant No. G1998020307) the National Natural Science Foundation of China (Grant No. 19631150).
文摘We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of $$u_i \left( {t + 1} \right) = ku_i \left( t \right) + \Delta t\left( {\sum\limits_{j = 1}^n {a_{ij} v_j \left( t \right) + a_i } } \right), i = 1,2, \cdots ,n,$$ , where the input-output function is defined as a generalized sigmoid function, such asv i =2/π arctan(π/2μiμi), $v_i = \frac{2}{\pi }arctan\left( {\frac{\pi }{2}\mu _i u_i } \right)$ and $v_i = \frac{1}{{1 + e^{ - u_i /\varepsilon } }},$ , etc. Numerical simulations are also provided to demonstrate the theoretical results.
