By 2013, smartphones will double their share of all cell phones to about 20%, reports In-Stat market research firm. Global smartphone growth this year will be strong globally, but even stronger in the U.S. market.

At present smartphones command about 10% of global handsets, but almost one-third of In-Stat’s survey respondents plan to obtain a smartphone the next time they upgrade their current phone.

“Strong demand is being driven by device manufacturers leveraging open OS device to re-invent the mobile phone experience. New and prospective smartphone buyers are drawn to new mobile applications, even though the median number of applications downloaded for all platforms, including the Apple iPhone, is relatively modest – below five applications per user for each platform,” says Frank Dickson, vice president of mobile Internet group at In-Stat.

The market research firm claims that there are several obstacles on they way of advanced mobile phones. According to In-Stat, smartphone security is still inadequate and is likely to be a source of problems for users and their employers.

Surprisingly, but smartphones with Linux OS (including Android) will see the highest growth and the second highest volume behind Symbian, In-Stat claims. Linux OS will outpace Windows Mobile, RIM and Apple iPhone OSX.