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In this paper, we study the stability of the zero equilibrium and the occurrence of flip bifurcation of the following system of difference equations: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2znb2+zn+c2ynek2−d2yn1+ek2−d2yn, zn+1=a3xnb3+xn+c3znek3−d3zn1+ek3−d3zn, where ai, bi,… Click to show full abstract
In this paper, we study the stability of the zero equilibrium and the occurrence of flip bifurcation of the following system of difference equations: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2znb2+zn+c2ynek2−d2yn1+ek2−d2yn, zn+1=a3xnb3+xn+c3znek3−d3zn1+ek3−d3zn, where ai, bi, ci, di, and ki, for i=1 , 2, and 3, are real constants and the initial values x0, y0, and z0 are real numbers. We study the stability of this system in the special case when one of the eigenvalues is equal to −1 and the remaining eigenvalues have absolute value less than 1, using the center manifold theory.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2020
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