Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering

By Steven H. Strogatz. 1995

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Quasiprobability behind the out-of-time-ordered correlator (2017, background): “Similarly, pitchfork plots signal the breaking of a symmetry in classical chaos [119].”
Critical slowing down as early warning for the onset and termination of depression (2013, unknown): “The term tipping point in such systems is informally used to refer to a family of catastrophic bifurcations in mathematical models (32), which in turn are simpli ﬁ cations of what characterizes the stability properties of real complex systems (25).”
Computational Sustainability (2011, unknown): “…systems theory provides tools for characterizing the dynamics and long term behavior of systems as a function of its system parameters, providing insights into the nonlinear system dynamics, identifying patterns and laws, in particular, bifurcations (Ellner and Guckenheimer 2006; Strogatz 1994).”
From Fair Decision Making To Social Equality (2018, background): “Therefore, the dynamics will approximately become an ODE with one variable, and oscillatory behavior cannot exist in first order one dimensional ODEs [22], then πt (1|B,AA+) will converge to some fixed point of the dynamics necessarily below πe .”
Efficient non‐linear proper orthogonal decomposition/Galerkin reduced order models with stable penalty enforcement of boundary conditions (2012, methodology): “While investigation of stability and sen sitivity of non-linear systems can sometimes be carried out analytically using techniques from non-line ar analysis [31, 15], numerical bifurcation techniques are required in general.”
Network resilience (2020, background): “For example, the Hopf bifurcation, which marks the transition from a stable system to an oscillatory system [227], is signaled by critical slowing”
Systems biology of stem cell fate and cellular reprogramming (2009, background): “Although Waddington viewed this epigenetic landscape as a qualitative conceptualization of development, the idea that cell types may be related to 'balanced states' of an underlying regulatory system bears a striking resemblance to the modern mathematical notion of attractors of dynamical system”