We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies.

In this work, we investigate the Lagrangians and potentials for two coupled damped Duffing oscillators both directionally and bi-directionally. We show that, although it is not always possible to define a potential in dissipative systems, the potential of our model can be defined if the damping coefficient has a logarithmic derivative form. It is possible to apply these results to the analysis of the dynamics of complex networks based on three-node motif configurations. As an example, we study numerically the dynamics for one of the thirteen different possible configurations. Here, the phenomenon of synchronization is observed in terms of the coupling parameter.

Tenebrio molitor larvae are a promising source for the next generation of liquid biofuels. However, the conditions and processes required for rearing this insect for biodiesel production need to be investigated. In this study, the effect of dextrose addition to an artificial diet in the oil and biodiesel yield was evaluated. Larvae were fed artificial diets modified with 3, 6, 9, and 15% dextrose. Survival rate, mean dry weight, and oil yield were registered. The 15% dextrose addition resulted in 75% survival, 25 mg individual dry weight, and 29% oil yield. The main components of this oil were palmitic acid (14%), oleic acid (37%), and linoleic acid (20%). With the addition of dextrose, the total saturated fatty acids increased 13% and the polyunsaturated fatty acids decreased 16% compared to the control. However, with the transesterification reaction, the fatty acid methyl esters remained similar for both treatments, with methyl oleate, methyl linoleate, and methyl linolenate as major components. This suggest that the transesterification reaction was incomplete, due to the oil/methanol ratio or the catalyst. Thus, even though a more balanced saturated/unsaturated fatty acid profile can be achieved through dextrose addition, another transesterification method should be tested to obtain a complete reaction.