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How to deal with non-equilibrium operating point

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#ordinary-differential-equations #dynamical-systems #control-theory #nonlinear-system #nonlinear-dynamics
165
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Lotka-Volterra equation (predator-prey): given any initial condition, how can one know the steady-state behavior?

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#ordinary-differential-equations #nonlinear-dynamics #steady-state
875
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Simple pendulum: How to solve the following second order nonlinear ODEs?

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#ordinary-differential-equations #classical-mechanics #nonlinear-dynamics
51
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System of nonlinear ODEs remains in positive cone

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#ordinary-differential-equations #nonlinear-system #nonlinear-dynamics
189
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Describe discrete-time Langevin dynamics by its stationary distribution

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#probability #stochastic-processes #dynamical-systems #markov-chains #nonlinear-dynamics
133
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Lyapunov Stability for a Nonlinear, Time-varying system

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#control-theory #nonlinear-system #stability-theory #nonlinear-dynamics #lyapunov-functions
64
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Classify the bifurcation that occurs at $\mu$ =0

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#dynamical-systems #nonlinear-dynamics
1.3k
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Nondimensionalization of the logistic equation.

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#ordinary-differential-equations #dynamical-systems #nonlinear-system #bifurcation #nonlinear-dynamics
55
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Geometric significance of a bifurcation point with algebraic multiplicity $2$?

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#ordinary-differential-equations #dynamical-systems #nonlinear-system #bifurcation #nonlinear-dynamics
131
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Solve sine and exponential nonlinear differential equation?

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#ordinary-differential-equations #nonlinear-system #nonlinear-dynamics
62
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Fundamental matrix of ODE system $\dot{x} = (At+B)x$

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#ordinary-differential-equations #nonlinear-dynamics
1.1k
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Improved model of a fishery: $\dot N=rN(1-\frac{N}{K})-H\frac{N}{A+N}$

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#ordinary-differential-equations #dynamical-systems #mathematical-modeling #biology #nonlinear-dynamics
131
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Nonlinear system of equation in real life

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#ordinary-differential-equations #nonlinear-dynamics
91
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How to calculate the averaged equations for the weakly nonlinear oscillator $\ddot x+x+\varepsilon (x\dot x^2)=0$?

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#ordinary-differential-equations #dynamical-systems #nonlinear-system #nonlinear-dynamics
231
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Relating the Nonlinear and Linear operators in the Homotopy Analysis Method

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#ordinary-differential-equations #taylor-expansion #homotopy-theory #approximation-theory #nonlinear-dynamics

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