Modeling the herd prey response to individualistic predators attacks

In this paper, we consider predators hunting on prey gathered in groups and in such way exhibiting the possibility of reducing the predators pressure. To model this feature, however, we depart from the Holling type II (HTII) response function, in that we assume that a sufficiently large set of prey could respond to individualistic attacks and therefore induce the predator to renounce. The basic idea is described at first in a simple two-populations predator-prey system. It is then expanded considering the generalist predators to deal with two prey. In the first case, both are gathered in herds, and in the second one, one of the two instead behaves individualistically. The net outcome is an enhanced survival for the prey with respect to both the herding cases without and with predators feeding satiation (i.e., using the HTII response)

Temporal and spatial patterns in a diffusive ratio-dependent predator-prey system with linear stocking rate of prey species

The ratio-dependent predator–prey model exhibits rich interesting dynamics due to the singularity of the origin. It is one of prototypical pattern formation models. Stocking in ratio-dependent predator–prey models is relatively an important research subject from both ecological and mathematical points of view. In this paper, we study the temporal, spatial patterns of a ratio-dependent predator–prey diffusive model with linear stocking rate of prey species. For the spatially homogeneous model, we derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction-diffusion model, firstly it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Then it is demonstrated that the model exhibits Hopf bifurcation which produces temporal inhomogeneous patterns. Finally, the non-existence and existence of positive non-constant steady-state solutions are established. We can see spatial inhomogeneous patterns via Turing instability, temporal periodic patterns via Hopf bifurcation and spatial patterns via the existence of positive non-constant steady state. Moreover, numerical simulations are performed to visualize the complex dynamic behavior

Temporal and spatial patterns in a diffusive ratio-dependent predator–prey system with linear stocking rate of prey species

The ratio-dependent predator–prey model exhibits rich interesting dynamics due to the singularity of the origin. It is one of prototypical pattern formation models. Stocking in a ratio-dependent predator–prey models is relatively an important research subject from both ecological and mathematical points of view. In this paper, we study the temporal, spatial patterns of a ratio-dependent predator–prey diffusive model with linear stocking rate of prey species. For the spatially homogeneous model, we derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction-diffusion model, firstly it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Then it is demonstrated that the model exhibits Hopf bifurcation which produces temporal inhomogeneous patterns. Finally, the non-existence and existence of positive non-constant steady-state solutions are established. We can see spatial inhomogeneous patterns via Turing instability, temporal periodic patterns via Hopf bifurcation and spatial patterns via the existence of positive non-constant steady state. Moreover, numerical simulations are performed to visualize the complex dynamic behavior

Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth

Allee effect in population dynamics has a major impact in suppressing the paradox of enrichment through global bifurcation, and it can generate highly complex dynamics. The influence of the reproductive Allee effect, incorporated in the prey's growth rate of a prey-predator model with Beddington-DeAngelis functional response, is investigated here. Preliminary local and global bifurcations are identified of the temporal model. Existence and non-existence of heterogeneous steady-state solutions of the spatio-temporal system are established for suitable ranges of parameter values. The spatio-temporal model satisfies Turing instability conditions, but numerical investigation reveals that the heterogeneous patterns corresponding to unstable Turing eigen modes acts as a transitory pattern. Inclusion of the reproductive Allee effect in the prey population has a destabilising effect on the coexistence equilibrium. For a range of parameter values, various branches of stationary solutions including mode-dependent Turing solutions and localized pattern solutions are identified using numerical bifurcation technique. The model is also capable to produce some complex dynamic patterns such as travelling wave, moving pulse solution, and spatio-temporal chaos for certain range of parameters and diffusivity along with appropriate choice of initial conditions Judicious choices of parametrization for the Beddington-DeAngelis functional response help us to infer about the resulting patterns for similar prey-predator models with Holling type-II functional response and ratio-dependent functional response

Qualitative dynamics of planar and spatial Lotka-Volterra and Kolmogorov systems

Ordinary differential equations are an important tool for the study of many real problems. In this thesis we focus in the qualitative dynamics of some ordinary differential systems, particularly, the Lotka-Volterra and Kolmogorov systems. We accomplish the study of some Lotka-Volterra systems on dimension three, which we characterize in two families of planar Kolmogorov systems. We give the complete classification of the global phase portraits in the Poincaré disk for those families. We also analyze the limit cycles of the three-dimensional Kolmogorov systems of degree three which appear through a zero-Hopf bifurcation. Some particular systems that model real problems in the field of population dynamics are also studied

What Joy from Misery: the Pleasures of Horror

This thesis investigates the allure of narrative genres, such as horror, that have historically been viewed as philosophically (and often morally) problematic owing to their negative content and the painful emotional responses they elicit. It departs from the majority of classical and contemporary solutions to the alleged paradox posed by such genres, in that it does not attempt to render their pleasures explicable by appealing to their fictive status, thematic or ideological meanings or the more comprehensibly-pleasurable meta-responses they inspire. Rather, this account suggests that we choose to consume stories – fictional and factual – that depict violent or distressing situations and evoke discomforting emotions, for the same reason we choose to engage with less obviously conflict-filled narratives. Fictions compel our attention insofar as they resemble potentially salient information, appealing to a set of deeply ingrained and unconscious cognitive biases that prompt us to attend to certain kinds of stimuli. We are capable of finding narrative genres such as horror, tragedy and the ‘misery memoir’ compelling – without, it is important to note, finding their content in any way pleasant – because we are predisposed to find some types of mental effort rewarding. While horror is often criticised – and defended – on the grounds that its pleasures must lie in slaking anti-social appetites, this thesis criticises the model of fiction’s appeal on which such assumptions are based. Instead it suggests that narrative pleasure characteristically resides in intellectual and emotional absorption or stimulation rather than any straightforward fulfilment of our real life desires. In support of this contention, this account incorporates analyses of a number of related topics, examining subjects such as the alleged rationality of the emotions, whether our attraction to non-factual narratives represents an adaptive trait and how fiction-making, criticism and consuming function as cultural practices