Stability analysis of systems of exponential difference equations

The studies carried out in this thesis are presented in five main sections. In the first section, a short introduction is made and the application areas of difference equations are mentioned. In the second section, literature studies related to systems of difference equations of exponential type are given. In the third section, the existence of a unique positive equilibrium, the boundedness, persistence and global attractivity of the positive solutions of the following system of difference equations x_(n+1)=ax_n+by_(n-1) e^(-x_n ), 〖 y〗_(n+1)=cy_n+dx_(n-1) e^(-y_n ),n∈N_0, where a,b,c,d are positive constants and the initial values x_(-1),x_0,y_(-1),y_0 are positive numbers, are examined. In the fourth section, the asymptotic behaviour of the positive solutions of system of difference equations 〖x_(n+1)=ay_n+bx_(n-1) e〗^(〖-y〗_n ), 〖y_(n+1)=cx_n+dy_(n-1) e〗^(〖-x〗_n ),n∈N_0, where a,b,c,d are positive constants and the initial values x_(-1),x_0,y_(-1),y_0 are positive numbers, are studied. In the last section, the results and discussions are given.