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...ve, python, etc to sketch the phase plane and plot trajectories x(t) and y(t). Compare what you generate to solutions generated in pplane8.m (seehttp:// ...ve, python, etc to sketch the phase plane and plot trajectories x(t) and y(t). Compare what you generate to solutions generated in pplane8.m (see http:/

...ta and J. M. Luck, Physical Review Letters '''65''', 393 (1990)</ref> <ref>T. Gilet, N. Vandewalle, and S. Dorbolo, Physical Review E '''79''', 055201(R x_p(t) = A[\sin(\omega t) + \sin(c \omega t)]

...onlinear ordinary differential equations in the variables x(t), y(t) and z(t), which give the voltages across the capacitors C1 and C2, and the intensit ...hua | first = Leon O. | authorlink = Leon O. Chua | coauthors = Matsumoto, T., and Komuro, M. | title = The Double Scroll | journal = IEEE Transactions

<math>\left<{\mathbf{V}(t)}\right> = \mathbf{v} + \dot{\gamma}\left<\tilde{\mathbf{g}}\mathbf{N}\righ <math>\mathbf{V}(t)</math> is the velocity of the particle, <math>\tilde{\mathbf{g}}</math> is

|last4=Kapitaniak |first4=T. |last4=Kapitaniak |first4=T.

...ta v}{\delta t}=-\frac{v}{Q \Omega}-\left[\frac{1}{\Omega^{2}}-\epsilon*cn(t,m)\right]*\sin{\theta}</math> <math>\frac{\delta \theta}{\delta t}=v</math>, <math>Q = \frac{\omega_{0}I}{b}</math>

...2 dimensional) system, the nonautonomous periodic term <math>f \cos(\omega t)</math> means that the equation actually determines a smooth vector field o ...>\phi</math> we have <math>\ddot{\phi}(t)=-\delta\dot{\phi}(t)-2\alpha\phi(t)</math>. We know that this gives us damped simple harmonic motion with freq

author = P. L. Kapitza, edited by T. Der Haar | ...\dot{\theta^{2}} + \dot{y}^2 + 2\ell\dot{y}\dot{\theta}\sin\theta)- m g [y(t) + \ell\cos(\theta)]

x(t) is the voltage across C1, y(t) is the voltage across C2, and z(t) is the current across L. &alpha; and &beta; depend on the values of the va :::<math>|&delta; Z(t)| = e^{&lambda;t} |Z(0)|</math>

...l, however, this does not result in a perfect synchronization <ref>Walker, T. J. (1969). Acoustic synchrony: two mechanisms in the snowy tree cricket. S 1969<ref name="walker69">Walker, T. J. (1969). Acoustic synchrony: two mechanisms in the snowy tree cricket. S

\(\epsilon (t)={ H }_{ 0 }\) \(\epsilon (t)={ H }_{ 0 }+\Delta H\sin { (\omega t) }\)

...cdot \left(\nabla\vec{v} + \nabla\vec{v}^T \right)+ \frac{1}{Fr}F(cos(2\pi t)-1)\mathbf{j}</math> ...tend to merge if they get to close to each other. In fact the radius ''R(t)'' of a hole is depends on acceleration ''a'', frequency ''f'', and the res

%\begin{figure}[t]

(i) $\displaystyle{d\phi \over{dt}} = {1\over{T}}$ models the change of phase of the oscillator ...reset to $0$ and perturbs the other oscillator by an amount, $\epsilon$, s.t. $\epsilon \in \mathbb{R}, \epsilon > 0$.

\tau=t\sqrt{\frac{g}{l}}