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O presente artigo tem por objetivo abordar as equações diferenciais impulsivas (EDIs) no aspecto de comportamento assintótico, de modo específico, este trabalho apresenta resultados sobre estabilidade em sistemas quase-lineares com... more
O presente artigo tem por objetivo abordar as equações diferenciais impulsivas (EDIs) no aspecto de comportamento assintótico, de modo específico, este trabalho apresenta resultados sobre estabilidade em sistemas quase-lineares com impulsos em tempos variáveis. Tais impulsos são de característica variável, pois dependem da solução do sistema em momentos específicos, determinados de acordo com o problema considerado. O estudo das EDIs é recente e composto, predominantemente, por trabalhos na literatura estrangeira, dessa forma, os resultados apontados neste texto trazem uma síntese do tratamento de soluções para estes sistemas impulsivos. A princípio, algumas definições significativas a respeito de estabilidade serão descritas para enfim enunciarmos e demonstrarmos teoremas de estabilidade para o sistema proposto.
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N. Kaldor's 1940 trade model combined with the M. Kalecki's remark (1935) pointing out the existence of a time lag between a decision of investment and its effect on the capital stock leads to a system of delay differential... more
N. Kaldor's 1940 trade model combined with the M. Kalecki's remark (1935) pointing out the existence of a time lag between a decision of investment and its effect on the capital stock leads to a system of delay differential equations proposed by Kraw-iec and Szydlowski in 1999, describing the behavior of the gross product and the capital stock. Under some conditions assumed by Krawiec and Szydlowski we investigate the occurrence of periodic orbits in the case where the savings and the investment have the same rate with respect to the national gross product. We take the delay as a constant inherent to the focused economy rather than what is current in the related literature, where the delay varies as a bifurcation parameter.
We are concerned with the Kaldor’s trade cycle model under the effect of a delay which represents a gestation lag between a decision of investment and its effect on the capital stock. Taking the adjustment coefficient in the goods market... more
We are concerned with the Kaldor’s trade cycle model under the effect of a delay which represents a gestation lag between a decision of investment and its effect on the capital stock. Taking the adjustment coefficient in the goods market as a bifurcation parameter, we achieve global branches of periodic solutions. In our setting the delay is a constant inherent to the specific economy.
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In 1995 for a linear oscillator, Myshkis imposed a constant impulse to the velocity, each moment the energy reaches a certain level. The main feature of the resulting system is that it defines a nonlinear discontinuous semigroup. In this... more
In 1995 for a linear oscillator, Myshkis imposed a constant impulse to the velocity, each moment the energy reaches a certain level. The main feature of the resulting system is that it defines a nonlinear discontinuous semigroup. In this note we study the orbital stability of a one-parameter family of periodic solutions and state the existence of a period-doubling bifurcation of such solutions.