Wide-area data transfers in high-performance computing and big data scenarios are increasingly being carried over dedicated network connections that provide high capacities at low loss rates. UDP-based transport protocols are expected to be particularly well-suited for such transfers but their performance is relatively unexplored over a wide range of connection lengths, compared to TCP over shared connections. We present extensive throughput measurements of UDP-based Data Transfer (UDT) over a suite of physical and emulated 10 Gbps connections. In sharp contrast to current UDT analytical models, these measurements indicate much more complex throughput dynamics that are sensitive to the connection modality, protocol parameters, and round-trip times. Lyapunov exponents estimated from the Poincaré maps of UDT traces clearly indicate regions of instability and complex dynamics. We propose a simple model based on the ramp-up and sustainment regimes of a generic transport protocol, which qualitatively illustrates the dominant monotonicity and concavity properties of throughput profiles and relates them to Lyapunov exponents. These measurements and analytical results together enable us to comprehensively evaluate UDT performance and select parameters to achieve high throughput, and they also provide guidelines for designing effective transport protocols for dedicated connections.