A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.
Este artigo compartilha uma ação educativa fundamentada na abordagem STEAM, a qual articula Ciências, Tecnologia, Engenharia, Artes e Matemática sob a perspectiva da melodia do pássaro Pitangus sulphuratus, o popular bem-te-vi. O cenário e ambiente de aprendizagem é o Parque Mãe Bonifácia, em Cuiabá (MT). O objetivo consiste em desenvolver propostas de atividades a partir da abordagem STEAM. A problemática caracterizou-se em como elaborar a abordagem STEAM a partir de um hóspede natural local do parque, o bem-te-vi. Alinhando se com essa ideia, com respaldo em uma perspectiva de Educação Científica, entrelaçam-se cinco áreas em dois conceitos estruturantes: a Bioacústica e o Biomimetismo. Assim, apresenta-se a articulação de conceitos imersos nesse conjunto de ideias para a contribuição de processos que potencializem, nos estudantes, as habilidades, visando a uma participação crítica e consciente em relação ao conhecimento, a partir do hóspede natural do Parque, o bem-te-vi.
Game Theory is a mathematical approach to the study of decision making between individuals when each outcome depends on the decisions of others, ie, one should not make an arbitrary decision, but decide based on what they think the decision of their "opponent" will be, knowing that they think the same. Developed by John von Neumann and Oskar Morgenstern in 1944 in the book Theory of Games and Economic Behavior, it had been very contested since its launch, but the works of a genius named John Nash, winner of the Nobel Prize in economics in 1994, ended these contestations. This work shows that the Game Theory was not limited to the field of economics, but expanded to other areas, such as biology, explaining strategies used by species to survive. As results are presented more than ten models based on the principles of Game Theory, among them the Prisoner's Dilemma, Ice Cream Vendors Game, Clean City Law and Warning Song between Bird.
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