LYAPUNOV functionsEQUATIONSLINEAR systemsFor continuous and discrete linear autonomous systems, we discuss the possibility ofchoosing the coefficients of the quadratic Lyapunov function that ensure the validity of thecondition of sign-negativity of its first derivative (first difference) with a given margin...
This indicates that our theorem will help reduce the amount of work searching for parameters causing chaos. We also generalize Theorem 2.1 to include systems with exponential functions. 展开 关键词: Theoretical or Mathematical/ chaos differential equations functions/ nonchaotic parameter regions simple ...
On the dynamical equations of conditional probability density functions, with applications to optimal stochastic control theory Let dx = g( x, u, t) dt + dz be a general dynamical system with control u and where z is Brownian motion ( dz dt = 尉 is white Gaussian noise). Let the loss...
Therefore, we have the following equations of coefficients: s 1 2 − s 2 s 3 + 2 s 1 + λ + μ μ ( s 3 − 1 ) = 0 , s 2 ( s 1 − s 4 ) + 2 s 2 + λ + μ μ ( s 4 − 1 ) = 0 , s 3 ( s 1 − s 4 ) + 2 s 3 − λ + μ λ + ...
If we use the suggested improvements and fit the mapped data to extended quadric: 𝑧̂=𝑎𝑥̂2+𝑏′𝑥̂𝑦̂+𝑐′𝑦̂2+ 𝑑′𝑥̂+𝑒′𝑦̂z^=ax^2+b′x^y^+c′y^2+ d′x^+e′y^, and solve the resulting system of linear equations, we finally obtain...
What Are the Intercepts of a Function? The intercepts can be of great help when graphing functions and equations. Intercepts are those points at which the graph crosses either the x- or the y-axis. More specifically, the x-intercept is the point at which a graph crosses the x-axis, and...
equations salt analysis acids, bases, and salts benzene organometallic compounds atomic number and mass number more maths pythagoras theorem prime numbers probability and statistics fractions sets trigonometric functions relations and functions sequence and series multiplication tables determinants and matrices ...
T-optimality has been applied to discriminate among various classes of models, ranging from polynomial models [5], [11], to Fourier regression models [10], Michaelis–Menten kinetic models [30], enzyme kinetics [2] and dynamic systems described by sets of ordinary differential equations [41],...
The shear rate module (Γ)206acan be represented by Equations 2 and 3 shown below. The apparent viscosity for a Carreau model is given by Equation 2. μ=μ∞+(μ0-μ∞)[1+(γγL)2](np-1)/2(Equation2) In Equation 2, μ0and μ∞are the low-shear and infinite shear...
equations for the curves were solved for phase as a function of discrete time intervals to determine the bits of information for three electrical phases to be stored in the memories of the zone controllers. For each whole lambda for a phase, there is a change in the binary instructions that...