## Nonlinear network modes in cyclic systems with applications to connected vehicles.(English)Zbl 1320.93012

Summary: In this paper, we propose a novel technique to decompose networked systems with cyclic structure into nonlinear modes and apply these ideas to a system of connected vehicles. We perform linear and nonlinear transformations that exploit the network structure and lead to nonlinear modal equations that are decoupled. Each mode can be obtained by solving a small set of algebraic equations without deriving the coefficients for any other mode. By focusing on the mode that is loosing stability, bifurcation analysis can be carried out. The techniques developed are applied to evaluate the impact of connected cruise control on the nonlinear dynamics of a connected vehicle system.

### MSC:

 93A30 Mathematical modelling of systems (MSC2010) 93A15 Large-scale systems 93C15 Control/observation systems governed by ordinary differential equations 93C10 Nonlinear systems in control theory 93C95 Application models in control theory 34A34 Nonlinear ordinary differential equations and systems 34C23 Bifurcation theory for ordinary differential equations 37G05 Normal forms for dynamical systems 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)

### Keywords:

connected cruise control; network dynamics; nonlinear modes

Knut; PDDE-CONT
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### References:

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