A new class of differential equations with impulses at instants dependent on preceding pulses. Applications to management of renewable resources

作者：Cordova Lepe Fernando^*; Pinto Manuel; Gonzalez Olivares Eduardo

来源：Nonlinear Analysis: Real World Applications , 2012, 13(5): 2313-2322.

DOI：10.1016/j.nonrwa.2012.01.026

• Impulsive differential equations
• Control
• Bioeconomics
• Renewable resources
• Stability
• Periodic solutions

In this paper, a new type of mathematical model to represent certain processes with impulsive dynamic behavior is introduced. The main assumption is that the next impulse time is determined by three fundamental elements: the present impulse time, the state at this moment, and the value to which this state is impelled. We also establish the basic results of existence, uniqueness and continuation of solutions for these new impulsive differential equations. It is observed that the new equations have interesting applications in Bioeconomics, and sometimes they include, the traditional impulsive equations in variable times.

• 出版日期2012-10