Abstract
In this paper, a perturbed traveling wave reduction of the Tricky–Biswas equation, which is used to describe the propagation of pulses in nonlinear optics, is considered. A stability analysis of the investigated ODE system without perturbation is carried out. The Melnikov function along the homoclinic orbit is constructed. It is found that in the studied system the necessary condition for occurrence of homoclinic chaos is always satisfied. A perturbation is added to the system to control the chaos obtained. Constraints on the parameters of the new system, at which homoclinic chaos is realized in it, are found. The attraction basins are plotted. It is found that their structure is fractal when the damping parameter values are less than the critical ones obtained by the Melnikov approach. The results of the numerical analysis go in agreement with those acquired theoretically.
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