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Juniper Networks Inc. (NASDAQ: JNPR) shares have risen more than 14% since Dec. 31. Activist investor Elliott Management thinks the networking company’s shares could easily jump to $35 to $40 and, at the time same, compete better against archrival Cisco Systems Inc. (NASDAQ: CSCO).

Elliott announced Monday that it has acquired a 6.2% stake in Juniper and offered a three-part proposal to boost shareholder value, not to mention the value of its investment. Shares rose 8.2% to $25.42, not far from a 52-week high.

The moves include cutting expenses by $200 million a year, buying back $2.5 billion in shares this year and $1 billion in 2015 (and adding special and regular dividends) and refocusing on its core networking business. It should sell or shut down its security business. The moves could boost the stock price 40% to 60%, Elliott said.

An Elliott presentation said the projected changes that could help Juniper regain a substantial portion of the market share it has lost to Cisco, Alcatel-Lucent S.A. (NYSE: ALU) and Chinese networking company Huawei.

That, in the turn, could put more pressure on Cisco, which also has struggled in the face of competition and slow growth in key markets, including Europe and China. Cisco stunned investors in November when it projected an 8% revenue decline in the quarter that ends on Jan. 31 and a 5% decline for the fiscal year that ends in July.

The shares fell nearly 16% by mid-December before coming back. They were at $22.33, up 0.5%, Monday afternoon. They are still trading down 0.3% in January, 16% below their 52-week high and 18% below their level 10 years ago.

Plus, as Barron’s noted this weekend, the networking business is facing a big challenge from what is called software defined networks. That means putting software on off-the-shelf servers. Cisco — and Juniper — typically offer hardware with the software already installed.

Juniper is second in networking behind Cisco, but shares of both companies have struggled compared with the stock market overall even since the March 2009 market bottom. The Nasdaq Composite Index is up about 230% since then. Juniper is up a bit more than 100%. Cisco is up 64%.

Barron’s thinks Cisco is already undervalued by some 20%. Its shares are selling at only 10 times forward earnings. That is a 30% discount to the forward price-to-earnings (P/E) ratio for the Standard & Poor’s 500 Index and around a 44% discount to Nasdaq Composite’s forward P/E.

Elliott’s timing looks deliberate. Shaygan Kheradpir, formerly with Barclays, just joined Juniper as chief executive. Elliott is no stranger to pressuring managements. It made a $19-a-share offer for Riverbed Technologies a week ago. The strategy is to induce another buyer to up the bidding.