Chaotic single neuron model with periodic coefficients with period two

Abstract

Our goal is to investigate the piecewise linear difference equation xn+1 = βnxn – g(xn). This piecewise linear difference equation is a prototype of one neuron model with the internal decay rate β and the signal function g. The authors investigated this model with periodic internal decay rate βn as a period-two sequence. Our aim is to show that for certain values of coefficients βn, there exists an attracting interval for which the model is chaotic. On the other hand, if the initial value is chosen outside the mentioned attracting interval, then the solution of the difference equation either increases to positive infinity or decreases to negative infinity.