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Hyperchaos remains one of the most complex behaviors in the bifurcation mechanisms and so far, only few hyperchaotic dynamics have been identified experimentally. The construction and design of complex models able to generate hyperchaotic attractors with wings on many rows and columns have become a source of interest for many fractal & chaos theorists, applied physicists and engineers. In this paper, we make use of a simple method, that consists on combining the fractal and fractional operator with L¨u system, in order to generate second class hyperchaotic attractors with wings on many rows and columns. Such a combination yields a modified initial value problem, that is solved both analytically and numerically. We then implement the proposed scheme to perform some graphical representations showing the second class types of attractors in the form n × m-wings, (n, m ∈ N), which appear to be hyperchaotic and exhibit a mirror symmetrical structure. The graphical simulations also depict a process where the lower and upper parts of the second class hyperchaotic attractors are seen to be moving away from the mirror symmetrical junction due to the parameter’s impact of the fractal-fractional operator. [ABSTRACT FROM AUTHOR]

This paper seeks to unveil the niche of delay differential equation in harmonizing low HIV viral haul and thereby articulating the adopted model, to delve into structured treatment interruptions. Therefore, an ordinary differential equation is schemed to consist of three components such as untainted CD4+ T-cells, tainted CD4+ T-cells (HIV) and CTL. A discrete time delay is ushered to the formulated model in order to account for vital components, such as intracellular delay and HIV latency which were missing in previous works but have been advocated for future research. It was divested that when the reproductive number was less than unity, the disease free equilibrium of the model was asymptotically stable. Hence the adopted model with or without the delay component articulates less production of virions as per the decline rate. Therefore CD4+ T-cells in the blood remains constant at δ 1 / δ 3 , hence declining the virions level in the blood. As per the adopted model, the best STI practice is intimated for compliance. [ABSTRACT FROM AUTHOR]

Not every chaotic system has the particularity of displaying attractors with a fractal structure. That is why strange attractors remain enthralling not only for their fractal structure, but also for their amazing chaotic and multi-scroll dynamics. In this work, we apply the non-local and non-singular kernel operator to a four-dimensional chaotic system with two equilibrium points and show the existence of various types of attractors, including the butterfly type and strange type. Recently, there have been virulent communications related to the validity or not of the index law in fractional differentiation with non-local operators. These discussions resulted in pointing out many important features of the Mittag-Leffler function used as kernel and suitable to describe more complex real world problems. This paper follows the same momentum by pointing out another important feature of the non-local and non-singular kernel operator applied to chaotic models. We solve the model numerically and discuss the bifurcation and period doubling dynamics that eventually lead to chaos (in the form of butterfly attractor). Lastly, we provide related numerical simulations which prove the existence of a chaotic fractal structure (strange attractors). [ABSTRACT FROM AUTHOR]

A model is proposed to understand the dynamics in a food chain (one predator‐two prey). Unlike many approaches, we consider mutualism (for defense against predators) between the two groups of prey. We investigate the conditions for coexistence and exclusion. Unlike Elettreby's (2009) results, we show that prey can coexist in the absence of predators (as expected since there is no competition between prey). We also show the existence of Hopf bifurcation and limit cycle in the model, and numerically present bifurcation diagrams in terms of mutualism and harvesting. When the harvest is practiced for profit making, we provide the threshold effort value ξ0 that determines the profitability of the harvest. We show that there is zero profit when the constant effort ξ0 is applied. Below (resp. above) ξ0, there will always be gain (resp. loss). In the case of gain, we provide the optimal effort ξ* and optimal steady states that produce maximum profit and ensure coexistence. Recommendations for resource managers As a result of our investigation, we bring the following to the attention of management: 1.In the absence of predators, different groups of prey can coexist if they mutually help each other (no competition among them).2.There is a maximal effort ξ0 to invest in order to gain profit from the harvest. Above ξ0, the investment will result in a loss.3.In the case of profit from harvest, policy makers should recommend the optimal effort ξ* to be applied and the optimal stock (x1*,x2*,y*) to harvest. This will guarantee maximum profit while ensuring sustainability of all species. [ABSTRACT FROM AUTHOR]