This paper proposes a general multiscroll Lorenz system family by introducing a novel parameterized nth-order polynomial transformation. Some basic dynamical behaviors of this general multiscroll Lorenz system family are then investigated, including bifurcations, maximum Lyapunov exponents, and parameters regions. Furthermore, the general multiscroll Lorenz attractors are physically verified by...

In this paper we prove that a higher-order differential equation with one middle term has every bounded solution oscillatory. Moreover, the behavior of unbounded solutions is given. Two other results dealing with positive solutions are also given.

In this article we consider the -stabilization of nth-order linear time-invariant dynamical systems using multiplicity-induced-dominancy-based controller design in presence delays input or output channels. A sufficient condition is given for dominancy a real root with multiplicity at least and n an integral factorization corresponding characteristic function. necessary -stabilizability analyzed...

In this paper, the authors give a simple review of closed-form, explicit, and recursive formulas related results for nth derivative power-exponential function xx, establish two closed-form explicit partial Bell polynomials at some specific arguments, present several new xx functions integer sequences.