In this paper, we consider the interaction between Rhinoceros Sondaicus, known as Javan Rhino, and Bos Javanicus, known as Javan Bull, at Ujung Kulon National Park. For years, the population of Javan Rhinos never exceeds their estimated carrying capacity, despite their vast habitat and there is no natural predator in the area. Both species naturally consume different food resources, hence there is no direct competition on food resource between the two species. This stagnant growth of Javan Rhino is suspected due to the territorial competition between the two species, in which the rapid growth of Javan Bull may reduce the territory of Javan Rhino and consequently reduce the carrying capacity of Javan Rhino. We construct a mathematical model of territorial competition between two species and show that domination of one species can lower the carrying capacity of the second species.

In this paper, the oscillations of an actuated, simply supported microbeam are studied for which it is assumed that the electric load is composed of a small DC polarization voltage and a small, harmonic AC voltage. Bending stiffness and mid-plane stretching are taken into account as well as small viscous or structural damping. No tensile axial force is assumed to be present. By using a multiple time-scales perturbation method, approximations of the solutions of the initial-boundary value problem for the microbeam equation are constructed. This analysis is performed without truncating the infinite series representation in advance as is usually done in the existing literature. It is shown in which cases truncation is allowed for this problem. Moreover, accurate and explicit approximations of the natural frequencies up to order ε 3 of the actuated microbeam are also obtained. Intriguing and new modal vibrations are found when the frequency of the harmonic AC voltage is (near) half or twice a natural frequency of the microbeam, i.e., near a superharmonic or a subharmonic resonance.

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A system of ordinary differential equations of a predator-prey type, depending on nine parameters, is studied. We have included in this model a nonmonotonic response function and time periodic perturbation. Using numerical continuation software, we have detected three codimension two bifurcations for the unperturbed system, namely cusp, Bogdanov-Takens and Bautin bifurcations. Furthermore, we concentrate on two regions in the parameter space, the region where the Bogdanov-Takens and the region where Bautin bifurcations occur. As we turn on the time perturbation, we find strange attractors in the neighborhood of invariant tori of the unperturbed system.2010 Mathematics Subject Classification. 37C60, 37G15, 34A34, 92D25.

In the last few decades, it has been reported that the population of Rhino (Rhinoceros Sondaicus) at the Ujung Kulon National Park has been reaching a stagnation at the number 50s, despite the existing territory can support a much larger number of Rhinos. Here, we construct a dynamical model representing the interaction between Rhino and Bull (Bos Javanicus) with Allee effect for the Javan rhinos population. This Allee effect may occur in the field, among others, due to the solitary behaviour of Rhino within large territory, imbalance of age structure and gender and difficulty of finding mates in Javan rhinos population which causes inbreeding in the population. In this paper, we follow the previous paper on the territorial competition between Javan rhino and Javan bull at Ujung Kulon National Park and add Allee effect factor on the Javan rhino's population. We give a proof on the boundedness of the solution and explanation on the bifurcations that occur in the model. One of these bifurcations plays an important role in the system. Some simulations and suggestion on how to improve the survival of Javan rhino is also included.