The generation and evolution of chaotic motions in a hybrid Rayleigh–Van der Pol–Duffing oscillator driven by parametric and amplitude-modulated excitation forces are investigated analytically and numerically. By using the Melnikov method, the conditions for the appearance of horseshoe chaos in our system are derived in the case where the modulation frequency [Formula: see text] and the forcing frequency [Formula: see text] are the same [Formula: see text]. The obtained results show that the chaotic region decreases and increases in certain ranges of frequency. The numerical simulations based on the basin of attraction of initial conditions validate the obtained analytical predictions. It is also found that in the case where [Formula: see text] is irrational, the increase of amplitude-modulated force accentuates the fractality of the basin of attraction. The global dynamical changes of our model are numerically examined. It is found that our model displays a rich variety of bifurcation phenomena and remarkable routes to chaos. In addition, the presence of the hybrid Rayleigh–Van der Pol damping force reduces the chaotic domain in the absence of amplitude-modulated force. But when the amplitude-modulated force acts on the system, the chaotic oscillations decrease and disappear. Further, the geometric shape of the chaotic attractors considerably decreases in the presence of the amplitude-modulated excitation force. On the other hand, the system presents transient chaos, torus-chaos and torus of different topologies when [Formula: see text] is irrational.

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Rapid population growth and major trends of world economy growth have led to significant energy needs in our country. Benin, Gulf of Guinea country, although with a significant coastal network powered by potential energy from breaking waves, has experienced a deficit and a critical energy instability, marked by recurrent power cuts and disruption of the national economy. To ensure the integration of this source of renewable energy in the Benin energy mix and sustainably reduce the energy deficit in progress, this work has aimed to study the dissipation of wave energy at the bathymetric breaking in the breakers zone of Cotonou coast. Sea conditions and the statistics parameters of the breaking waves under perturbation effect of the seabed were evaluated to predict the beginning of the breaking. The modeling is based on the Navier-Stokes equation in which the viscosity and the interactions between the molecules of the oceanic fluid are neglected. The nonlinear wave dispersion relation is also used. The results obtained for this purpose showed that water particles have an almost parabolic motion during their fall; their velocity is higher than those of the early breaking. In this area, the waves dissipate about 80% of their energy: it generates turbulence which leads to a strong setting in motion of sediments.