A nonlinear modification of the Cauchy problem Dtf(t, z) = θDzf(t, z) + zD 2 zf(t, z), t ∈ IR+ = [0,+∞), z ∈C, θ ≥ 0, f(0, z) = g(z) ∈ L is considered. The set L consists of Laguerre entire functions, which one obtains as a closure of the set of polynomials having real nonpositive zeros only in the topology of uniform convergence on compact subsets of C. The modification means that the time hal...

Grey-box’ models take advantage of physical insight about the dynamical system in question. This reduces uncertainty and facilitates the remaining system identification process. Here a grey-box system identification (GBSI) method for nonlinear dynamical systems is presented, which first establishes a linear model (the ‘white box’) using a priori knowledge and conventional tools, and then adds a...

We present some integrable time-dependent systems of classical dynamics, and we apply the results to the equation ẍ + f(t)x = 0, with f a positive non-decreasing differentiable function; some of the results are extended to the nonlinear case. Moreover we investigate the conditions for the solutions to be bounded and we study their asymptotic behaviour.

In this paper, we consider the nonlinear delay dynamic system x(t) = p(t)f1(y(t)), y (t) = −q(t)f2(x(t− τ)). We obtain some necessary and sufficient conditions for the existence of nonoscillatory solutions with special asymptotic properties of the system. We generalize the known results in the literature. One example is given to illustrate the results.

The stochastic response of dynamic systems has been an area of considerable interest for some time in the analysis of risk and structural reliability. The authors, in previous work, have developed a method which can analyze the response of linear multi-degree-of-freedom systems to completely general data-based nonstationary excitations in a highly efficient and analytical form. The authors exte...

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic differential equations and thus may shed lights on predictability in nonlinear systems with model uncertainty.

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

In this paper, the nonlinear dynamical systems are solved by using the homotopy analysis method (HAM).The approximation solution of this equation is calculated in the form ofa series which its components are computed easily. The existence anduniqueness of the solution and the convergence of the proposed methodare proved.The results obtained here demonstrate that the HAM is an effective and robu...

We introduce a formal decomposition method for efficiently computing the parametric normal form of nonlinear dynamical systems with multiple parameters. Recently introduced notions of formal basis style and costyle are applied through formal decomposition method to obtain the simplest parametric normal form for degenerate nonlinear parametric center. The necessary formulas are derived and imple...